Bevacizumab and Erlotinib or Sorafenib as First-Line Therapy in Treating Patients With Advanced Liver Cancer

DISEASE CHARACTERISTICS: * Pathologically confirmed advanced hepatocellular carcinoma (HCC) * Childs-Pugh class A * CLIP score ≤ 5 * Not a candidate for curative surgical resection or loco-regional therapy * Measurable disease as per RECIST 1.1 criteria, defined as ≥ 1 previously unirradiated, bidimensionally measurable lesion ≥ 20 mm by CT scan or MRI (triphasic spiral CT scan or MRI employing a "liver protocol" image capture technique required) * Bone lesions, ascites, and pleural effusions are not considered measurable lesions * No fibrolamellar HCC * No known brain metastases * No prior organ transplantation PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * Absolute neutrophil count ≥ 1,500/mm³ * Platelet count ≥ 75,000/mm³ * Hemoglobin ≥ 9 g/dL * Transaminases ≤ 5 times upper limit of normal (ULN) * Total bilirubin ≤ 2.0 times ULN * PT ≤ 1.8 times ULN * Prolonged INR allowed for patients who require full dose anticoagulation * Creatinine ≤ 2.0 mg/dL OR creatinine clearance ≥ 45 mL/min * Urine protein \< 2+ by urine dipstick OR urine protein ≤ 1 g by 24-hour urine collection * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 12 weeks after completion of study treatment * Able to take and absorb oral medication * No active infection requiring parenteral therapy * No known HIV or AIDS * No uncontrolled blood pressure (BP), defined as systolic BP ≥ 150 mm Hg and/or diastolic BP ≥ 100 mm Hg * No uncontrolled or significant cardiovascular disease, including any of the following: * Myocardial infarction within the past 6 months * Uncontrolled angina within the past 6 months * New York Heart Association class II-IV congestive heart failure * Grade 3 cardiac valve dysfunction * Cardiac arrhythmia not controlled by medication * Stroke or transient ischemic attack within the past 6 months * Arterial thrombotic event of any type within the past 6 months * No significant or symptomatic vascular disease (e.g., aortic aneurysm, aortic dissection, or peripheral vascular disease) within the past 6 months * No decompensated liver disease as evidenced by clinically significant ascites refractory to diuretic therapy, hepatic encephalopathy, or coagulopathy not corrected by conservative measures * No grade 3 bleeding esophageal or gastric varices within the past 2 months * Prior variceal bleeding allowed provided patient has undergone banding or sclerotherapy and there has been no evidence of bleeding for 2 months * No gastric varices ≥ grade 2 * No hemoptysis (i.e., ≥ ½ teaspoon of bright red blood per episode) within the past month * No evidence of bleeding diathesis or coagulopathy * No concurrent uncontrolled illness, including, but not limited to, a history of or current evidence of unexplained nephrotic syndrome or other severe illness/disease that would preclude study participation * No history of hypertensive crisis or hypertensive encephalopathy * No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 6 months * No serious, non-healing wound, active ulcer, or untreated bone fracture * No significant traumatic injury within the past 28 days * No history of allergy to bevacizumab, erlotinib hydrochloride, sorafenib tosylate, or related compounds * No other primary malignancy within the past 5 years, except carcinoma in situ of the cervix or urinary bladder or nonmelanoma skin cancer * No mental incapacitation or psychiatric illness that would preclude study participation * Not incarcerated or compulsorily detained (i.e., involuntarily incarcerated) for treatment of either a psychiatric or physical illness (e.g., infectious disease) PRIOR CONCURRENT THERAPY: * Prior surgery, local ablation, trans-arterial hepatic artery embolization, or trans-arterial chemoembolization are allowed provided the lesion(s) have progressed since treatment OR there are additional measurable, untreated lesions present * No prior systemic therapy for HCC * No prior organ transplantation * More than 7 days since prior minor surgical procedures, fine needle aspirations, or core biopsies (excluding placement of a vascular access device) * More than 28 days since any prior therapy * More than 28 days since prior and no concurrent major surgical procedure or open biopsy * More than 28 days since prior and no concurrent participation in another experimental drug study * No other concurrent anticancer or antitumor therapy, including chemotherapy, radiotherapy, immunotherapy, or hormonal anticancer therapy * No other concurrent investigational agents * No concurrent warfarin (other types of anticoagulation allowed)