Ph I Vorinostat in the Treatment of Advanced Staged Oropharyngeal Squamous Cell Carcinoma

Inclusion Criteria: * Patients with histologically confirmed unresectable or borderline resectable squamous cell carcinoma of the oropharynx will be eligible for enrollment to the clinical trial * Oropharyngeal sites of tumor include tonsil, soft palate, base of tongue, lateral and posterior pharyngeal wall * Patient must be AJCC (American Joint Committee on Cancer) Stage III (T3N0, T1-2N1) or Stage IVa (T1-4N2-3M0, T4N0-1 M0) and be either unresectable or borderline resectable * No prior therapy for the tumor, including extensive surgery, radiation therapy, chemotherapy, immunotherapy, targeted therapy or any other investigational agents; surgical biopsy prior to beginning the study is allowable * Prior malignancies at sites other than the head and neck are allowable if there has been greater than or equal to a 3 year disease free interval; basal cell carcinoma of the skin and in-situ cervix dysplasias are allowable within this 3 year interval if completely resected * There must be documentation of evaluable tumor within four weeks of beginning therapy * ECOG (Eastern Cooperative Oncology Group) Performance Status 0-2, (Karnofsky \> 60%) * Ability to understand and the willingness to sign a written informed consent * Patient must have normal liver and bone marrow function * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Prothrombin Time or INR (international normalized ratio) =\< 1.5x upper limit of normal (ULN) unless receiving therapeutic anticoagulation * Partial thromboplastin time (PTT) =\< 1.2 times the ULN unless the patient is receiving therapeutic anticoagulation * K levels preferred normal limits with no clinical abnormalities * Mg levels preferred normal limits with no clinical abnormalities * Creatinine =\< ULN OR Calculated creatinine clearance \>= 50 mL/min * Serum total bilirubin =\< 1.5 X ULN * AST (SGOT) and ALT (SGPT) =\< 2.5 X ULN * Alkaline Phosphatase =\< 2.5 X ULN * No known malabsorption syndrome * Female patients of childbearing potential must be willing to use birth control; the 2 birth control methods can be either 2 barrier methods or a barrier method plus a hormonal method to prevent pregnancy, used throughout the study starting with visit 1 * The following are considered adequate barrier methods of contraception: diaphragm, condom (by the partner) or sponge; other methods of contraception such as copper intrauterine device or spermicide may be used * Appropriate hormonal contraceptives will include any registered and marketed contraceptive agent that contains an estrogen and/or a progestational agent (including oral, subcutaneous, intrauterine, or intramuscular agents); female patient of childbearing potential has a negative serum pregnancy test β-hCG within 7 days prior to receiving the first dose of vorinostat * Male patients agree to use an adequate method of contraception for the duration of the study * The patient must have a life expectancy of at least 12 weeks * Patients on coumadin therapy are eligible for study Exclusion Criteria: * Major surgery or trauma occurring within 28 days of starting the trial * History of allergic reactions attributed to compounds similar in chemical or biological composition to Vorinostat or other agents used in this study * Gastrointestinal tract disease or previous surgical procedures resulting in an inability to take oral or enteral medication or a requirement for IV alimentation * Pregnant women; breast feeding should be discontinued during treatment * Active peptic ulcer disease * Uncontrolled comorbid illness including but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina, untreated or new cardiac arrhythmia, psychiatric or social condition which would limit the patient's understanding of and compliance with the study * Prisoners and other vulnerable populations * Patients who have had prior treatment with an HDAC inhibitor (e.g., romidepsin (Depsipeptide), NSC-630176, MS 275, LAQ-824, belinostat (PXD-101), LBH589, MGCD0103, CRA024781, etc) * Patients who have received compounds with HDAC inhibitor-like activity, such as valproic acid, as anti-tumor therapy should not enroll in this study; patients who have received such compounds for other indications, e.g. valproic acid for epilepsy, may enroll after a 30-day washout period * Patient is currently participating or has participated in a study with an investigational compound or device within 30 days of initial dosing with study drug(s) * Patients with known active viral hepatitis or known HIV infection