For oropharynx primary tumors, the patient must have negative human papillomavirus (HPV) status of the tumor as determined by p protein expression using immunohistochemistry (IHC)
Biopsy proven squamous cell carcinoma that is HPV and/or p positive
Any human papillomavirus (HPV) status or smoking history is permitted; oropharyngeal cancer patients are required to undergo HPV testing with p immunohistochemistry and/or confirmatory HPV polymerase chain reaction (PCR) or in situ hybridization (ISH) testing
Histological confirmation of human papillomavirus (HPV) positive (+) squamous cell carcinoma of the oropharynx; HPV positivity will be defined as positive staining for p on immunohistochemistry (IHC)
Human Papillomavirus (HPV)+ disease of the oropharynx
HPV-positive status ( In HNSCC patients only)
Patients who are HPV-positive by deoxyribonucleic acid (DNA) test
Patients with HPV-positive or p-positive oropharyngeal squamous cell carcinoma (SCCA)
Participants must have histologically or cytologically confirmed and identified resectable primary squamous cell carcinoma of the oropharynx that is HPV  positive or positive for any high risk HPV subtype (i.e., , , , etc.) as determined by PCR at the central laboratory. Patients must have p+ status as determined by IHC performed or reviewed at the central laboratory. Both p and HPV status must be determined prior to post-surgical adjuvant treatment assignment. Tissue from the primary site must be available for biomarker studies after surgery
Known human papillomavirus (HPV) status
Patients with vulvar cancer originating from differentiated vulvar intraepithelial neoplasia (d-VIN), as opposed to vulvar intraepithelial neoplasia of usual type, are excluded; vulvar squamous cell carcinoma originating from differentiated VIN (d-VIN) is HPV negative; however, rare cases of HPV positive d-VIN can occur; patients are not excluded if their tumor has tested positive for HPV or there is no documentation of prior VIN type
Diagnosis of P/HPV-ISH positive OPSCC
Have tumor tissue for PD L expression testing, and for oropharyngeal cancer have results from testing of HPV p status.
All patients with oropharyngeal SCCHN must be tested for HPV (by p and/or HPV in situ hybridization [ISH] or polymerase chain reaction [PCR])
Tumor sample must be available for HPV p and PD-L testing and if oropharyngeal, must be tested for HPV p
Subjects with histologically- or cytologically-documented incurable human papillomavirus (HPV)-positive OPSCC. HPV- serotype will be assessed by Cervista assay.
Patients vulvar HSIL that is not HPV-+ or is associated with multiple types of high-risk HPV are not eligible
Low-risk HPV+ disease, defined as meeting all of the following criteria:\r\n* Patients with HPV+ by fluorescence in situ hybridization (FISH) and/or p\r\n* Smoking history =<  pack years\r\n* Stage T-N-b, TN
Patients must have pathologically confirmed HPV-positive head and neck squamous cell carcinoma of the oropharynx; confirmed HPV-positive disease of other subsites are uncommon but also eligible
HPV testing must be compliant with the following criteria:\r\n* p IHC positivity is sufficient to enroll and initiate treatment (p IHC interpretation to follow guidelines by Jordan and Lingen et al)\r\n* p IHC positivity is to be validated using an HPV polymerase chain reaction (PCR) during the induction phase; this is essential as HPV genotype influences treatment arm allocation, with non-HPV HPV strains being considered high risk
Prior HPV vaccination
Histologically or cytologically confirmed HNSCC of the oral cavity (OC; more than % patients have HPV negative cancer) or oropharynx (about -% of patient have HPV positive cancer)
HPV status in oropharyngeal carcinomas; while HPV status (e.g. via p) does not have to be known prior to consenting, the HPV status (e.g. using p immunohistochemistry [IHC]) needs to be established prior to start of therapy
Must be considered intermediate or high risk:\r\n* Oropharynx intermediate risk patients include those who have all of the following:\r\n** Human papillomavirus (HPV)/p (positive [+]) disease, a significant tobacco smoking history (>  pack years) and Nb-N disease OR\r\n** HPV (negative [-]) disease, =<  years of smoking and large tumors (T-T)\r\n* Oropharynx high risk patients include those who are either:\r\n** HPV (-) with >  years of smoking, OR\r\n** HPV (-), =<  years of smoking and T disease\r\n* Oral cavity, larynx, hypopharynx are considered high/intermediate risk (regardless of HPV, p or smoking status)
Histologically confirmed diagnosis of squamous cell carcinoma of the oropharynx, stage IVa, p-positive on immunohistochemistry (determination of HPV status using p as surrogate is standard of care)
patients whose lesions are HPV+
Subject has pathologic confirmation of recurrent or metastatic HNSCC, regardless of human papillomavirus (HPV) status or PDL- status
Tumor HPV status established
Participants must have histologically or cytologically confirmed squamous cell carcinoma of the oropharynx or unknown primary that is high risk human papillomavirus (HPV) positive as determined by p immunohistochemistry (IHC) testing and/or HPV in situ hybridization (ISH) / polymerase chain reaction (PCR)
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Carcinoma of the oropharynx associated with HPV as determined by p protein expression using immunohistochemistry (IHC) performed by a Clinical Laboratory Improvement Act [CLIA] approved laboratory; using p antibody obtained from Roche mtm laboratories AG (CINtec, clone EH) is recommended
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: No prior radiation above the clavicles
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Patients must not have evidence of extensive or matted/ fixed pathologic adenopathy on preoperative imaging
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Hemoglobin >  g/dL
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Lymphocyte count >  x ^/mL
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Neutrophil count >  x ^/mL
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Platelet count > , x ^/mL
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Serum albumin > . g/dL
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Alkaline phosphatase <  x ULN
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Calculated creatinine clearance >  mL/min
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Willing and able to give informed consent and adhere to protocol therapy
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: ECOG performance status < 
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Negative urine/serum pregnancy test (females only) at the time of screening and within  hours of study treatment, if applicable
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Prior surgery, radiation therapy, or chemotherapy other than biopsy or emergency procedure required for supportive care
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Any medical contraindications or previous therapy that would preclude treatment with either nivolumab or IRX- or the surgery, reconstruction or adjuvant therapy required to treat the oropharynx tumor appropriately
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Clinical status of either subject or tumor such that administration of neoadjuvant nivolumab or IRX- before surgery would be medically inappropriate
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Tumor of the oral cavity
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Any investigational agent within the previous  days
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Daily administration of systemic immunosuppressive therapy or corticosteroids (except in physiological doses for hormone deficiency) during the previous  days
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Myocardial infarction within the last  months
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Evidence of distant metastases (M disease) or other concurrent primary malignancy
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Known infection with hepatitis B, hepatitis C, or HIV
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Signs or symptoms of systemic bacterial infection (use of antibiotics to treat superficial infection or contamination of tumor shall not, by itself, be considered evidence of infection)
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Stroke or other symptoms of cerebral vascular insufficiency within the last  months
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Allergy to ciprofloxacin (or other quinolones), acetylsalicylic acid
HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA: Prior axillary dissection
Patients who have HPV negative squamous cell carcinoma of unknown primary in cervical lymph node
Histologically or cytologically confirmed diagnosis of cervical, anal, penile, vulvar, or vaginal cancer positive for HPV- and/or HPV- by the Cervista assay. Tumors may be positive for more than  HPV subtype as long as HPV- and/or HPV- is present. Note: for the first  patients, only cervical, vulvar, or vaginal cancers will be enrolled.
Known human papillomavirus (HPV) status for oropharyngeal primary tumors
Have histological diagnosis of squamous cell cancer of the head & neck with confirmation of HPV positivity or squamous, non-squamous, adenosquamous, carcinoma or adenocarcinoma of the cervix which HPV positivity is not required
Tumor sample must be available for HPV p and PD-L testing
Tumors must be staged T-, Nb-, M (human papillomavirus positive [HPV]+ or HPV negative [-]); patients with HPV+ tumors should have at least one high risk feature such as T, N, or smoking history of >  pack years
Pretreatment tumor biopsy with sufficient tumor for HPV or p analysis is required; the tumor must be HPV(+) or p(+)
Documentation of results from testing of human papilloma virus (HPV) status for oropharyngeal cancer.
Patients with primary oropharynx HNSCC must be HPV (-) according to local institutional definition using either p immunohistochemistry or HPV testing
Carcinoma of the neck of unknown primary site origin (regardless of HPV/p status) is eligible
Phase II only:\r\nArms  and : disease must be determined to be HPV-unrelated; HPV-unrelated SCCHN is defined as either p-negative oropharyngeal squamous cell carcinoma (OPSCC) or non-OPSCC (larynx, hypopharynx, oral cavity) or p-negative unknown primary SCC presenting with a level  or  neck node; p will be assessed by IHC; a specimen showing any staining will be considered p-positive\r\nArm : disease must be HPV-related SCCHN (defined as OPSCC or unknown primary presenting with a neck mass that is either p positive or HPV in situ hybridization [ISH] or polymerase chain reaction [PCR] positive)
Positive HIV test at screening (except in cohort , HPV-associated cancers)
Subjects with histologically- or cytologically-documented incurable human papillomavirus (HPV)- positive solid tumors including oropharyngeal squamous cell carcinoma (OPSCC), cervical, vulvar, vaginal, anal, penile cancer; incurable HPV- solid tumors are defined as tumors which are not curable by salvage approaches including resection and/or re-irradiation; HPV- serotype will be assessed by Cervista assay
Have results from testing of HPV status for oropharyngeal cancer
Recurrent and/or metastatic HPV-related carcinoma of the cervix, anus, vagina, vulva, penis, or oropharynx; the cancer diagnosis must be confirmed by slide review in the Memorial Sloan-Kettering Cancer Center (MSKCC) Department of Pathology; HPV positive status must be demonstrated by HPV in situ-hybridization (ISH) and/or by p immunohistochemistry (IHC)\r\n* Note: for cervix squamous cancer, HPV ISH test or p IHC test is not required
At least one prior systemic therapy regimen for R/M HPV-related carcinoma
Patients must have pathologically confirmed HPV-positive squamous cell carcinoma
HPV testing must follow the following criteria\r\n* HPV testing using an E/E based assay is preferred, and does not require any validation (e.g. HPV in situ hybridization [ISH] or HPV E/E polymerase chain reaction [PCR])\r\n* For oropharyngeal tumors p immunohistochemistry (IHC) positivity is sufficient to enroll and initiate treatment (p IHC interpretation to follow guidelines by Jordan/Lingen et al ); it is recommended that p IHC positivity is validated at a later point (during or after treatment) using an E/E based test at the University of Chicago and provided slides will be used\r\n* For non-operative (OP) tumors accurate HPV testing (i.e. ISH, or E/E based testing) is required for enrollment and treatment initiation
Histological confirmation of HPV+ squamous cell carcinoma of the oropharynx; HPV positivity will be defined as positive staining for p on immunohistochemistry (IHC)
Subjects must have a histologically or cytologically confirmed metastatic or unresectable\r\n* Solid tumor (for phase I dose escalation portion), OR\r\n* virally mediated tumors (such as with HPV+ nasopharyngeal cancer, HPV+ cervical cancer) and liposarcoma (for expansion cohort)
Tumor positive for infection with human papillomavirus (HPV) virus type  or other types such as per Johns Hopkins (JH) Pathology assessment
Patients with a previously untreated, T or T, N-Nb transorally resectable (as determined by the treating surgeon), histologically proven HPV positive, squamous cell carcinoma (SCC) of the oropharynx
For oropharynx or nasopharynx primary lesions, documentation of viral status is required (e.g. high risk human papilloma virus [HPV] sub-type polymerase chain reaction [PCR], p IHC, HPV in situ hybridization [ISH], Epstein-Barr virus-encoded small ribonucleic acid [EBER], etc); tests done on primary tumor specimens from date of initial diagnosis at outside institutions are sufficient to meet this criterion
Patients must have HPV positive HNSCC containing activating PIKCA mutations.
History of previous therapeutic HPV vaccination;
Measurable metastatic or locally advanced refractory/recurrent malignancies that are HPV- or HPV- HPV positive by in situ hybridization (ISH) or polymerase chain reaction (PCR) or any cancer from the uterine cervix
Histologically or cytologically confirmed diagnosis of HNSCC associated with HPV by a p immunohistochemistry (IHC) assay or HPV- or HPV- positive by nucleic acid testing.
Patients must have histologically confirmed head and neck cancer (squamous cell histology), and may be poorly differentiated, stages IVA, IVB, and select cases of stage III or any stage that meets criterion\r\n* Human papilloma virus (HPV) status is required prior to randomization for oropharyngeal primary tumors, other anatomic sites will be classified as HPV- unless requested per the treating physician\r\n* Epstein Barr virus (EBV) status is required prior to randomization for nasopharyngeal primary tumors, other anatomic sites will be classified as HPV- unless requested per the treating physician
Documented HPV/ EBV-positive tumor as determined by a local laboratory for Part B and Part B pembrolizumab combination viral-positive expansion cohorts only
Human papilloma virus (HPV) status in tumor has been documented using tumor immunohistochemistry for HPV-p or other accepted test
Biopsy proven squamous cell carcinoma that is HPV and/or p positive
Women who report no history of co-testing (Pap and HPV) within the last five years
Previous prophylactic HPV vaccination
Survey response indicated no prior history of HPV vaccination
Agrees to return to participating institution for  HPV vaccine injections
Allergy to any component of the HPV vaccine including yeast and aluminum
HPV positive by the GeneXpert hrHPV assay with HPV, HPV /, or HPV//// detected; Note: participants who are hrHPV positive with only HPV/ or HPV /// detected are not eligible
Prior HPV vaccination
Primary oropharyngeal HNSCC which is HPV (+) as defined by p IHC
Women with an abnormal pap test, positive human papillomavirus (HPV) test or any history of cervical dysplasia
Prior use of an HPV vaccine  \r\n* Women in the vaccine-eligible age range cannot have received vaccine prior to enrollment, but will be offered HPV vaccination at the end of the study; in brief, we are interested in the efficacy of intervention in preventing HPV in the absence of HPV vaccination, since most women worldwide who might utilize intervention will not have been vaccinated; this includes United States (US) women in the vaccine catch-up - year old age group (beyond the age groups eligible for Vaccines for Children- funded vaccination) who have so far had very low (< %) vaccine uptake; it also includes the entire group of US women >  years of age; moreover, it includes women of all ages in developing countries, who most need an HPV prevention strategy, but may never be vaccinated; it should be noted that delaying vaccination in women - years of age by one year is safe and reasonable, since there is insufficient data to establish a recommendation for or against universal vaccination in this age group as concluded by an American Cancer Society expert panel, which includes the Principal Investigator (PI) of this protocol, Dr. Mark Einstein; it is anticipated that if the intervention gel is efficacious, HPV vaccinated women would need to be studied in a similar future trial with power analysis taking into account vaccine effectiveness as well
Patients whose lesions are HPV+ by polymerase chain reaction (PCR) (treatment groups , ,  and ); group  (imiquimod alone:  HPV+ subjects,  HPV- subjects)
Has not received any doses of HPV vaccine
Patients who have ONLY HPV  OR HPV  AND  and no other High-Risk HPV by Cobas test will be included.
Receipt of (e.g. Gardasil or Cervarix) HPV preventative vaccines within  years of study enrollment
Previous vaccination against HPV
Human Papilloma Virus (HPV) status
Not having received any doses of the HPV vaccine
Prior receipt of Gardasil or other HPV vaccine
Previous vaccination against HPV or planned administration of another HPV vaccine during the study other than that foreseen in the protocol.
if they test positive for oncogenic HPV infection, but display normal cervical cytology at their concluding HPV- study end visit;
if they are pregnant so that no cervical sample can be taken at their concluding HPV- study end visit;
Human papilloma virus (HPV) negative tumor for patients with oropharyngeal cancers.