Eligibility Criteria:
Inclusion Criteria:
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Pathologically confirmed (histology or cytology), p16-negative (by immunohistochemistry \[IHC\]) stage II, III, or IVA squamous cell cancer of the oral cavity (excluding lip)
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Disease is surgically resectable with curative intent
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Hemoglobin \> 9 g/dL
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Lymphocyte count \> 500/µL
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Neutrophil count \> 1500/µL
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Platelet count \> 100,000/µL
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Serum albumin \> 3.0 g/dL
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Aspartate aminotransferase (AST/serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT/ serum glutamate pyruvate transaminase \[SGPT\]) \< 3 x the upper limits of normal (ULN)
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Alkaline phosphatase \< 2 x ULN
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Prothrombin time (PT) and partial thromboplastin time (PTT) \< 1.4 x ULN
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Calculated creatinine clearance \> 50 mL/min
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Willing and able to give informed consent and adhere to protocol therapy
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Eastern Cooperative Oncology Group (ECOG) performance status \< 2
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Female of childbearing potential (less than 12 months post-menopausal) or male with a partner of childbearing potential either agrees to be abstinent or uses a medically acceptable form of birth control during the study and for a period of 1 year
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Negative urine/serum pregnancy test (female participants only) at the time of screening and within 24 hours of study treatment, if applicable
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Stage 1 (T1/2 N1) squamous cell carcinoma of the oropharynx associated with HPV as determined by p16 protein expression using immunohistochemistry (IHC) performed by a Clinical Laboratory Improvement Amendments \[CLIA\] approved laboratory
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: No prior radiation above the clavicles
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Patients with a history of a curatively treated malignancy must be disease-free for at least two years prior to entry on study except for carcinoma in situ of cervix, melanoma in-situ (if fully resected), and/or non-melanomatous skin cancer
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Patients must not have evidence of extensive or "matted/fixed" pathologic adenopathy on preoperative imaging
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Hemoglobin \> 9 g/dL
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Lymphocyte count \> 500/µL
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Neutrophil count \> 1500/µL
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Platelet count \> 100,000/µL
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Serum albumin \> 3.0 g/dL
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Aspartate aminotransferase (AST/ SGOT) and alanine aminotransferase (ALT/ SGPT) \< 3 x the upper limits of normal (ULN)
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Alkaline phosphatase \< 2 x ULN
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Prothrombin time (PT) and partial thromboplastin time (PTT) \< 1.4 x ULN
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Calculated creatinine clearance \> 50 mL/min
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Willing and able to give informed consent and adhere to protocol therapy
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: ECOG performance status \< 2
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Female of childbearing potential (less than 12 months post-menopausal) or male with a partner of childbearing potential either agrees to be abstinent or uses a medically acceptable form of birth control during the study and for a period of 1 year
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Negative urine/serum pregnancy test (female participants only) at the time of screening and within 24 hours of study treatment, if applicable
Exclusion Criteria:
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Prior surgery, radiation therapy, or chemotherapy other than biopsy or emergency procedure required for supportive care
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-cytotoxic T-lymphocyte associated protein 4 (anti-CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Prior treatment with cetuximab or epidermal growth factor receptor (EGFR) inhibitors in any treatment setting
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Any medical contraindications or previous therapy that would preclude treatment with either nivolumab, IRX-2, the surgery, reconstruction or adjuvant therapy required to treat the oral tumor appropriately
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Clinical status of either subject or tumor such that administration of 10 day neoadjuvant IRX-2 before surgery would be medically inappropriate
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Primary tumor of the oropharynx
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Tumor involvement of the following sites or any of these signs or symptoms likely to be associated with T4b cancer:
* Involvement of pterygopalatine fossa, maxillary sinus, or facial skin
* Gross extension of tumor to the skull base
* Pterygoid plate erosion
* Sphenoid bone or foramen ovale involvement
* Direct extension to involve prevertebral fascia
* Extension to superior nasopharynx or Eustachian tube
* Direct extension into the neck with involvement of the deep neck musculature (neck node fixation)
* Suspected invasion (encasement) of the common or internal carotid arteries; encasement will be assessed radiographically and will be defined as tumor surrounding the carotid artery 270 degrees or greater
* Direct extension of neck disease to involve the external skin
* Direct extension to mediastinal structures
* Regional metastases to the supraclavicular neck (low level VB and IVB)
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Any investigational agent within the previous 30 days
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Daily administration of systemic immunosuppressive therapy or corticosteroids (except in physiological doses for hormone deficiency) during the previous 30 days
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Chronic anticoagulation, not including aspirin, but including heparins, warfarin, oral anticoagulation or other platelet function inhibitors
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Symptomatic cardiopulmonary disease (including congestive heart failure and hypertension), coronary artery disease, serious arrhythmia or chronic lung disease; patients with these conditions who are stable with relatively minor symptoms and who are appropriate candidates for surgical treatment of their tumor need not be excluded
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Myocardial infarction within the last 3 months
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Evidence of distant metastases (M1 disease) or other concurrent primary malignancy
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Known infection with hepatitis B, hepatitis C, or human immunodeficiency virus (HIV)
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Signs or symptoms of systemic infection (use of antibiotics to treat superficial infection or contamination of tumor shall not, by itself, be considered evidence of infection
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Stroke or other symptoms of cerebral vascular insufficiency within the last 3 months
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Allergy to ciprofloxacin (or other quinolones) and acetylsalicylic acid
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Previous diagnosis of invasive cancer from which the individual is NOT disease-free AND that has required treatment within the past 5 years, except for superficial skin, cervical cancer in-situ, well-differentiated thyroid or early stage prostate or bladder cancer (i.e., treatment with curative intent and long term disease-free expectations)
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: Prior axillary dissection
* ORAL CAVITY SQUAMOUS CELL CARCINOMA COHORT: History of pneumonitis or interstitial lung disease
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Prior surgery, radiation therapy, or chemotherapy other than biopsy or emergency procedure required for supportive care
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Prior treatment with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Any medical contraindications or previous therapy that would preclude treatment with either nivolumab or IRX-2 or the surgery, reconstruction or adjuvant therapy required to treat the oropharynx tumor appropriately
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Tumor of the oral cavity
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Tumor involvement of the following sites or any of these signs or symptoms likely to be associated with T4b cancer:
* Involvement of pterygopalatine fossa, maxillary sinus
* Gross extension of tumor to the skull base
* Pterygoid plate erosion
* Sphenoid bone or foramen ovale involvement
* Direct extension to involve prevertebral fascia
* Extension to superior nasopharynx or Eustachian tube
* Direct extension into the neck with involvement of the deep neck musculature (neck node fixation)
* Suspected invasion (encasement) of the common or internal carotid arteries; encasement will be assessed radiographically and will be defined as tumor surrounding the carotid artery 270 degrees or greater
* Direct extension of neck disease to involve the external skin
* Direct extension to mediastinal structures
* Regional metastases to the supraclavicular neck (low level VB and IVB)
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Any investigational agent within the previous 30 days
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Daily administration of systemic immunosuppressive therapy or corticosteroids (except in physiological doses for hormone deficiency) during the previous 30 days
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Chronic anticoagulation, not including aspirin, but including heparins, warfarin, oral anticoagulation or other platelet function inhibitors
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Symptomatic cardiopulmonary disease (including congestive heart failure and hypertension), coronary artery disease, serious arrhythmia or chronic lung disease; patients with these conditions who are stable with relatively minor symptoms and who are appropriate candidates for surgical treatment of their tumor need not be excluded
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Myocardial infarction within the last 3 months
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Evidence of distant metastases (M1 disease) or other concurrent primary malignancy
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Known infection with hepatitis B, hepatitis C, or HIV
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: 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 COHORT: Stroke or other symptoms of cerebral vascular insufficiency within the last 3 months
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Allergy to ciprofloxacin (or other quinolones), acetylsalicylic acid
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Previous diagnosis of invasive cancer from which the individual is NOT disease-free AND that has required treatment within the past 5 years, except for superficial skin, cervical cancer in-situ, well-differentiated thyroid or early stage prostate or bladder cancer (i.e., treatment with curative intent and long term disease-free expectations)
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: Prior axillary dissection
* HPV-ASSOCIATED OROPHARYNX SQUAMOUS CELL CARCINOMA COHORT: History of pneumonitis or interstitial lung disease