Phase I/II Study of Postoperative Adjuvant Chemoradiation for Advanced-Stage Cutaneous Squamous Cell Carcinoma of the Head and Neck (cSCCHN)

Inclusion Criteria: * Patients must have primary or recurrent advanced-stage (III/IV) squamous cell carcinoma of the skin of the face, ear, scalp or neck or of the lip * A biopsy or preserved representative tumor block is required to confirm the diagnosis * Patients must be surgical candidates with resectable disease; macroscopic complete resection of all tumor must be planned with curative intent * Patients must be willing to receive postoperative radiation therapy and treatment with study drugs * Both men and women and members of all races and ethnic groups will be included * Life expectancy of greater than 12 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count \>= 1,500/microliter(uL) * Hemoglobin \>= 9 g/dL * Platelets \>= 100,000/uL * International normalized ratio (INR) \< institutional upper limit of normal (ULN) * Total bilirubin =\< 1.5 x institutional ULN * Aspartate aminotransferase (AST) serum glutamic oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic pyruvic transaminase (SGPT) =\< 2.5 X institutional ULN * Creatinine =\< 1.5 X institutional ULN * Fasting blood glucose \< 125 mg/dL at baseline * Patients-both males and females-with reproductive potential (i.e., menopausal for less than 1 year and not surgically sterilized) must practice effective contraceptive measures throughout the study; women of childbearing potential must provide a negative pregnancy test (serum or urine) within 14 days prior to registration * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients with known distant metastasis * Patients who have had prior radiation treatment of the index cancer or area of disease * Patients who have received any other investigational medication within 6 weeks of enrollment, or who are scheduled to receive an investigational drug during the course of the study * Prior treatment with EGFR inhibitor for index cancer * Prior treatment with an IGF-1R antagonist (small molecule inhibitor or antibody) * Breast-feeding, pregnancy or of childbearing potential (including less than two years postmenopausal) and unable to confirm adequate contraception due to possible risk to fetus or infant * Insulin-dependent and non-insulin dependent diabetes mellitus including any metformin or insulin use on an ongoing basis prior to enrollment * Known severe hypersensitivity to erlotinib, other small molecule inhibitors of EGFR, or its excipients * Hepatitis B or C infection (acute or chronic), known human immunodeficiency virus (HIV), or active uncontrolled infection, because of possible risk of lethal infection when treated with marrow suppressive therapy * History of uncontrolled cardiac disease such as unstable angina pectoris, myocardial infarction within prior 6 months, untreated coronary artery disease, uncontrolled congestive heart failure, or cardiomyopathy with decreased ejection fraction * Uncontrolled peptic or gastric ulcer disease or gastrointestinal bleeding within prior 6 months * Corrected QT interval (QTc) \> 450 msec; congenital long QT syndrome or previous history of QTc prolongation as a result from other medication * Presence of left bundle branch block (LBBB); QTc with Bazett's correction that is unmeasurable, or \>= 450 msec on screening electrocardiogram (EKG) * Any concomitant medication that may cause QTc prolongation or concomitant medication that is associated with Torsades de Pointes * Psychiatric illness/social situations that would limit compliance with study requirements * Active smokers unwilling to quit smoking during treatment * Use of the potent cytochrome P450 3A4 (CYP3A4) and cytochrome P450 1A2 (CYP1A2) inhibitors is not allowed; other less potent CYP3A4 and CYP1A2 inhibitors/inducers are not excluded * Participation in another investigational trial while on this study is not allowed * History of poorly controlled gastrointestinal disorders including acute diverticulitis, intra-abdominal abscess, gastrointestinal obstruction, Crohn's disease, ulcerative colitis or other diseases which have the potential for bowel perforation * Other malignancies except for resected cervical cancer in situ