Erlotinib and Cetuximab With or Without Bevacizumab in Treating Patients With Metastatic or Unresectable Kidney, Colorectal, Head and Neck, Pancreatic, or Non-Small Cell Lung Cancer

Inclusion Criteria: * One of the following histologically confirmed diagnoses: * Renal cell cancer * Clear cell histology * Metastatic or unresectable disease AND meets 1 of the following criteria: * Recurrent disease * Refractory to interleukin-2 (IL-2)- or interferon-based therapy * Previously untreated AND not a candidate for IL-2-based therapy * Colorectal, head and neck, pancreatic, or non-small cell lung cancer * Metastatic or unresectable disease * Progression after prior standard treatment * No evidence of CNS disease, including the following (part 2 only): * Primary brain tumor * Brain metastases * Paraffin embedded tumor blocks available * Performance status - ECOG 0-2 * Performance status - Karnofsky 60-100% * More than 12 weeks * Absolute neutrophil count ≥ 1,500 mm\^3 * Platelet count ≥ 100,000 mm\^3 * Bilirubin ≤ 1.5 mg/dL * AST and ALT ≤ 2.5 times upper limit of normal (ULN) (5 times ULN if liver metastasis is present) * PTT and INR ≤ 1.5, unless receiving full-dose warfarin (part 2 only) * Creatinine ≤ 1.5 times ULN * Creatinine clearance ≥ 60 mL/min * Calcium \< 10 mg/dL (hypocalcemic agents allowed) * No proteinuria\* * Protein \< 1 g on 24-hour urine collection\* * No unstable angina pectoris * No cardiac arrhythmia * No symptomatic congestive heart failure * None of the following are allowed for part 2: * Myocardial infarction within the past 6 months * New York Heart Association class II-IV heart disease * Serious cardiac arrhythmia requiring medication * Peripheral vascular disease ≥ grade II * Recent history of cerebrovascular accident * Uncontrolled hypertension (blood pressure ≥ 150/85 mm Hg despite medication) * Other clinically significant cardiovascular disease * No gastrointestinal (GI) tract disease resulting in an inability to take oral medication * No GI tract disease resulting in a requirement for IV alimentation * No active peptic ulcer disease * No history of allergic reaction attributed to compounds of similar chemical or biologic composition to study drugs * No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies (part 2 only) * No ongoing or active infection * No active infection requiring parenteral antibiotics (part 2 only) * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 2 months after study treatment * No significant traumatic injury within the past 28 days (part 2 only) * No history of abnormalities of the cornea (e.g., dry eye syndrome, Sjögren's syndrome, or congenital abnormality \[e.g., Fuch's dystrophy\]) * No other malignancy within the past 3 years except nonmelanoma skin cancer or carcinoma in situ of the breast or cervix * No psychiatric illness or social situation that would preclude study compliance * No serious or non-healing wound ulcer or bone fracture (part 2 only) * No other uncontrolled illness * See Disease Characteristics * More than 4 weeks since prior immunotherapy * No prior cetuximab * No prior bevacizumab * Concurrent epoetin alfa or darbepoetin alfa allowed * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) * More than 4 weeks since prior radiotherapy * No prior surgical procedures affecting absorption * Prior nephrectomy or resection of metastatic lesions allowed provided patient has fully recovered * More than 7 days since prior core biopsy\* * More than 28 days since prior major surgery or open biopsy\* * No concurrent major surgery\* * Recovered from all prior therapy * No prior erlotinib * Concurrent bisphosphonates allowed * Concurrent full-dose anticoagulants allowed provided the following criteria are met (part 2 only): * In-range INR (usually between 2 and 3) AND on a stable dose of warfarin or low molecular weight heparin * No active bleeding * No pathological conditions that carry a high risk of bleeding (e.g., tumor involving major vessels or varices) * No other concurrent investigational agents * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent anticancer therapy