Sorafenib Tosylate and Erlotinib Hydrochloride in Treating Patients With Locally Advanced, Unresectable, or Metastatic Gallbladder Cancer or Cholangiocarcinoma

Inclusion Criteria: * Cytologically or pathologically confirmed gallbladder carcinoma or cholangiocarcinoma * No ampullary carcinoma * Locally advanced unresectable or distant metastatic disease * Measurable disease * Patients with biliary obstruction must have decompression of the biliary tree by ERCP and stenting or percutaneous drainage * No prior systemic treatment for metastatic or unresectable locally advanced disease * No known brain metastases * Zubrod performance status of 0-1 * Leukocyte count ≥ 3,000/mm\^3 * ANC ≥ 1,000/mm\^3 * Platelet count ≥100,000/mm\^3 * Total serum bilirubin ≤ 1.5 times upper limit of normal (ULN) * For patient who had decompression of the biliary tree within the past 14 days, stability of the bilirubin level needs to be confirmed with two measurements within 5 to 7 days of each other * Serum albumin ≥ 2.5 g/dL * AST and ALT ≤ 2.5 times ULN (≤ 5 times ULN for liver metastases) * Creatinine clearance ≥ 60 mL/min * Not pregnant or nursing * Fertile patients must agree to use effective contraception * No active biliary sepsis * No bleeding diathesis * No uncontrolled or clinically significant cardiovascular disease, including any of the following: * Myocardial infarction within the past 6 months * Uncontrolled angina within the past 6 months * NYHA class II-IV congestive heart failure * Grade 3 cardiac valve dysfunction * Cardiac arrhythmia not controlled by medication * History of stroke or transient ischemic attack within the past 6 months * History of arterial thrombotic event of any type in the past 6 months * No uncontrolled hypertension, as evidenced by systolic BP ≥ 150 mm Hg or diastolic BP ≥ 100 mm Hg, within the past 28 days * Must be able to swallow and tolerate oral medications * No gastrointestinal tract disease or prior abdominal surgery that results in an inability to absorb oral medication * No other prior malignancy except adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease-free within the past 3 years * No concurrent grapefruit or its juice * At least 6 months since 1 adjuvant or neoadjuvant regimen of chemotherapy, hormonal therapy, immunotherapy, radiotherapy (to \< 25% of bone marrow only), or chemoradiotherapy before documented recurrence or metastatic disease * No prior treatment with any antiangiogenic agent or any EGFR inhibitors for any reason * Concurrent multiple anti-hypertensive medications allowed * No plans to receive concurrent chemotherapy, hormonal therapy, radiotherapy, immunotherapy, or any other therapy, including herbal or alternative medications for treatment of cancer