Gabapentin, Methadone, and Oxycodone With or Without Venlafaxine Hydrochloride in Managing Pain in Participants With Stage II-IV Squamous Cell Head and Neck Cancer Undergoing Chemoradiation Therapy

Inclusion Criteria: * Patients who are eligible for chemoradiation therapy of the head and neck. * Patients must have adequate renal function to undergo platinum based chemotherapy. This will mean a baseline creatinine level (Cr) no greater than 1.5 times the upper limit of normal. * Have a pathologic diagnosis of squamous cell carcinoma of the head and neck region * Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2. * Ability to swallow and/or retain oral or per tube medication. * Patients of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Patient or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure. Exclusion Criteria: * Patients who have previously been treated with surgery or radiation for head and neck cancer and/or are being treated for recurrent head and neck cancer. * Patients with known brain metastases will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Any patients prescribed medications for chronic and/or long term pain and/or neuropathy will be excluded, including patients under treatment of a pain specialist or substance-abuse programs. Acute post-op medications are allowed if the patient has discontinued them prior to initiating study. * Any patients prescribed a selective serotonin reuptake inhibitor (SSRI), serotonin and norepinephrine reuptake inhibitor (SNRI), tricyclic antidepressant (TCA), monoamine oxidase inhibitors (MAOIs), dextromethorphan, triptan, tryptophan supplements, IV methylene blue, linezolid or any other medication that may increase risk of serotonin syndrome, as deemed by the investigator?s opinion. * Any patients with suspected or known, current or recent (within last 5 years) use of cocaine, amphetamines, lysergic acid diethylamide (LSD), 3,4- methylenedioxymethamphetamine (MDMA), or any other drug of abuse that may increase risk of serotonin syndrome, as deemed by the Investigator?s opinion. * Any patients with history of suicide-related events, or those exhibiting a significant degree of suicidal ideation. * Patients with acute narrow-angle glaucoma. * Uncontrolled concurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant or nursing female patients. * Unwilling or unable to follow protocol requirements. * Any condition which in the investigator?s opinion deems the patient an unsuitable candidate to receive study drug. * Received an investigational agent within 30 days prior to enrollment. * Patients on dialysis or with transplanted organs. * Patients already enrolled on other studies of systemic pain control agents.