Inclusion Criteria:

          -  REGISTRATION TO SURGERY (ARM S)

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1

          -  Patients must have newly diagnosed, histologically or cytologically confirmed squamous
             cell carcinoma or undifferentiated carcinoma of the oropharynx; patients must have
             been determined to have resectable oropharyngeal disease; patients with primary tumor
             or nodal metastasis fixed to the carotid artery, skull base or cervical spine are not
             eligible

          -  Patients must have American Joint Committee on Cancer (AJCC) TNM tumor stage III, IV
             a, or IV b (with no evidence of distant metastases) as determined by imaging studies
             (performed < 4 weeks prior to pre-registration) and complete head and neck exam; the
             following imaging is required: computed tomography (CT) scan with IV contrast or
             magnetic resonance imaging (MRI)

          -  Patients must have biopsy-proven cyclin-dependent kinase inhibitor 2A (p16)+
             oropharynx cancer; the histologic evidence of invasive squamous cell carcinoma may
             have been obtained from the primary tumor or metastatic lymph node; it is required
             that patients have nodal stage N1-N2b confirmed by clinical or radiographic methods
             (clinically N0 patients are not eligible)

          -  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; using p16 antibody obtained from
             Roche mtm laboratories AG (CINtec, clone E6H4) is recommended

          -  No prior radiation above the clavicles

          -  Patients with a history of a curatively treated malignancy must be disease-free for at
             least two years except for carcinoma in situ of cervix and/or non-melanomatous skin
             cancer

          -  Patients with the following within the last 6 months prior to pre-registration must be
             evaluated by a cardiologist and/or neurologist prior to entry into the study

          -  Patients must not have evidence of extensive or "matted/fixed" pathologic adenopathy
             on preoperative imaging

          -  Absolute neutrophil count >= 1,500/mm^3

          -  Platelets >= 100,000/mm^3

          -  Total bilirubin =< the upper limit of normal (ULN)

          -  Calculated creatinine clearance must be > 60 ml/min using the Cockcroft-Gault formula

          -  Women must not be pregnant or breast-feeding due to the teratogenicity of
             chemotherapy; all females of childbearing potential must have a blood test or urine
             study within 2 weeks prior to registration to rule out pregnancy; a female of
             childbearing potential is any woman, regardless of sexual orientation or whether they
             have undergone tubal ligation, who meets the following criteria: has not undergone a
             hysterectomy or bilateral oophorectomy; or has not been naturally postmenopausal for
             at least 24 consecutive months (i.e., has had menses at any time in the preceding 24
             consecutive months)

          -  Patient must not have an intercurrent illness likely to interfere with protocol
             therapy or prevent surgical resection

          -  Patients must not have uncontrolled diabetes, uncontrolled infection despite
             antibiotics or uncontrolled hypertension within 30 days prior to pre-registration

          -  REGISTRATION/RANDOMIZATION TO STEP 2 - ARMS A, B, C AND D AND REGISTRATION TO STEP 3

          -  Histopathologic assessment of surgical pathology must include examination for
             perineural invasion (PNI) and lymphovascular invasion (LVI) and reported as absent or
             present; the absence or presence of extracapsular extension (ECE) requires gross and
             microscopic assessment and is defined to be:

               -  Absent (negative or nodal metastasis with smooth/rounded leading edge confined to
                  thickened capsule/pseudocapsule),

               -  Present - minimal (tumor extends =< 1 mm beyond the lymph node capsule), or

               -  Present - extensive (gross, tumor extends > 1 mm beyond the lymph node capsule
                  (includes soft tissue metastasis)

          -  Patients must have ECOG performance status 0 or 1

          -  Patient must be registered/randomized within 5-7 weeks following surgery

          -  Women of childbearing potential and sexually active males are strongly advised to use
             an accepted and effective method of contraception