Erlotinib, Docetaxel, and Radiation Therapy in Treating Patients With Locally Advanced Head and Neck Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed locally advanced (stage III or IV) squamous cell carcinoma of the head and neck without distant metastatic disease * No prior chemotherapy, radiation therapy, or investigational anti-tumor drug * Measurable disease within 4 weeks prior to registration according to the recommended RECIST response criteria * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Absolute neutrophil count \>= 1,500/ul * Platelets \>= 100,000/ul * Hemoglobin \>= 10 mg/dL * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) =\< 5 x ULN when alkaline phosphatase is =\< ULN * Alkaline phosphatase =\< 5 x ULN when AST or ALT =\< ULN * Prothrombin time within normal institutional limits * Creatinine within normal institutional limits or creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * No clinically significant heart disease (including NYHA class III or IV heart disease, significant arrhythmias requiring medication, symptomatic coronary artery disease, myocardial infarction within the previous six months, second or third degree heart block or bundle branch block) * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control) prior to study entry and for the duration of study participation; men and women of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months thereafter; women of childbearing potential must have a negative pregnancy test; 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 willingness to sign a written informed consent document Exclusion Criteria: * All histologies other than squamous cell carcinoma * Salivary gland and paranasal sinus squamous cell carcinoma * Patients who have had prior chemotherapy or radiotherapy * Patients may not be receiving any other investigational agents * Patients with known brain metastases or direct cerebral invasion by tumor 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; patients with intracranial extension (but without cerebral involvement) may still be eligible to participate * History of allergic reactions attributed to compounds of similar chemical or biologic composition to OSI-774 or docetaxel, including other drugs formulated with polysorbate 80 * No pre-existing peripheral neuropathy \>= grade 2 * Uncontrolled intercurrent 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 women are excluded from this study; breastfeeding should be discontinued if the mother is treated on this protocol * HIV positive patients are excluded from participation * Patients with history of any other malignancy (except squamous cell or basal cell cancer of the skin or CIS of cervix) are ineligible unless a period of 5 years has elapsed since treatment of the previous cancer and the patient has remained continuously disease free * Patients who are felt to be poorly compliant