Erlotinib and Radiation Therapy With or Without Cisplatin in Treating Patients With Mouth or Throat Cancer

Inclusion Criteria: * Patients with clinical findings consistent with a diagnosis of squamous cell carcinoma of the OC or OP, as determined by the head and neck surgeon, may be recruited to the study prior to diagnostic biopsy; patients must have a histologically confirmed diagnosis of squamous cell carcinoma of OC or OP prior to proceeding with treatment * Oropharyngeal sites include base of tongue, tonsil, soft palate, and oropharyngeal wall * Oral cavity sites include oral tongue, buccal mucosa, floor of mouth, retromolar trigone, alveolar ridge, hard palate and mucosal lip * Patients must be AJCC stage II (T2N0) or III (T1-2N1) (AJCC fifth edition, 1997) for part A of the study, and must be AJCC stage III (T3N 0-1) or IV (T1-4N2-3M0, T4N0-1M0) for part B of the study * Priority for study entry will be given to patients with easily accessible tumor and who consent to repeat biopsy; study entry will not be restricted to patients who agree to further biopsies; if a patient enrolls on study and later refuses biopsy (excluding diagnostic), he/she may remain on study * Patients with operable or inoperable tumors will be eligible * No prior therapy for the tumor, including chemotherapy, radiation therapy, immunotherapy, EGFR targeted therapies, or any other investigational agents * Prior malignancies of sites other than the head and neck are allowed if disease free interval \>= 3 years; basal cell carcinomas of the skin and in situ cervical dysphagias are allowed within this three year interval if completely resected * Documentation of evaluable tumor less than or equal to four weeks before treatment start * ECOG performance status = 0, 1 or 2 (Karnofsky \>= 60%) * Life expectancy of greater than or equal to 6 months * Leukocytes \>= 3,000 * Absolute neutrophil count \>= 1,500 * Platelets \>= 100,000 * Total bilirubin within normal institutional limits unless due to hemolysis or Gilbert's syndrome * AST(SGOT)/ALT(SGPT) =\< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * APTT/INR within normal institutional limits; patients who have abnormalities in APTT/INR that are correctable after administration of vitamin K are eligible * No uncontrolled diabetes mellitus as glucose must be within a consistently normal range for each patient in order to standardize PET scan interpretations * No known malabsorption syndrome * G-tube dependent patients are eligible * The effects of OSI-774 on the developing human fetus at the recommended therapeutic dose are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control) for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients with known brain involvement should 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 * History of allergic reactions attributed to compounds of similar chemical or biologic composition to OSI-774 or other agents used in study * Major surgery or significant traumatic injury occurring within 28 days prior to treatment * Abnormalities of the cornea based on history (e.g., dry eye syndrome, Sjögren's syndrome), congenital abnormality (e.g., Fuch's dystrophy), abnormal slit-lamp examination using a vital dye (e.g., fluorescein, Bengal Rose), and/or an abnormal corneal sensitivity test (Schirmer test or similar tear production test) * Gastrointestinal tract disease resulting in an inability to take oral or enteral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, untreated or new cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because OSI-774 is an epidermal growth factor inhibitor with the potential for teratogenic or abortifacient effects based on the data suggesting that EGFR expression is important for normal organ development; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with OSI-774, breastfeeding should be discontinued if the mother is treated with OSI-774 * Because patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with OSI-774; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated * Patients on Coumadin are excluded from the study because of reports of interactions between the study drug and Coumadin