Sorafenib Tosylate, Bevacizumab, Irinotecan Hydrochloride, Leucovorin Calcium, and Fluorouracil in Treating Patients With Metastatic Colorectal Cancer

Inclusion Criteria: * This trial is intended for gastrointestinal malignancies appropriate for irinotecan-based therapy; histologic proof of cancer that is now unresectable; if prior therapy was received, patients must have shown progressive disease during prior treatment or within 6 months of their most recent therapy * Measurable disease or non-measurable disease * Absolute neutrophil count (ANC) \>= 1500/uL * Platelet (PLT) \>= 100,000/uL * Hemoglobin (Hgb) \>= 9.0 gm/dL * Total bilirubin =\< upper limit of normal (ULN) * Alkaline phosphatase =\< 3 x ULN * Aspartate aminotransferase (AST) =\< 3 x ULN OR AST =\< 5 x ULN if liver involvement * International normalized ratio (INR) \< 1.5 unless patients are receiving anti-coagulation therapy; patients receiving anti-coagulation therapy with an agent such as warfarin or heparin are allowed to participate if INR =\< 3.0 * Urine protein creatinine (UPC) ratio \< 1 or urine dipstick \< 2+ * NOTE: urine protein must be screened by urine analysis for UPC ratio or by dipstick; for UPC ratio \>= 1.0, 24-hour urine protein must be obtained and the level should be \< 1000 mg * Creatinine =\< 1.5 x ULN * Calculated creatinine clearance must be \>= 45 mL/min using the Cockcroft-Gault formula * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Ability to provide informed consent * Willing to return to Mayo Clinic for follow up * Life expectancy \>= 84 days (3 months) * Women of childbearing potential only: negative pregnancy test done =\< 7 days prior to registration Exclusion Criteria: * Known standard therapy for patient's disease that is potentially curative Note: * Prior treatment with irinotecan, 5-fluoruracil or bevacizumab is allowed * Prior treatment with sorafenib is not allowed * Inadequately controlled hypertension (systolic blood pressure of \> 150 mmHg or diastolic pressure \> 100 mmHg on anti-hypertensive medications) * Prior history of hypertensive crisis or hypertensive encephalopathy * History of myocardial infarction or unstable angina =\< 6 months prior to registration or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Heart failure New York Heart Association classification III or IV * Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks =\< 6 months prior to registration * Any hemorrhage/bleeding event \> grade 3 =\< 4 weeks prior to registration * Evidence or history of bleeding diathesis (greater than normal risk of bleeding) or coagulopathy (in the absence of therapeutic anticoagulation); NOTE: patients on full-dose anticoagulants are eligible provided the patient has been on a stable dose for at least 2 weeks of low molecular weight heparin or warfarin and has an INR in the range of 2-3; aspirin doses \> 325 mg PO daily are not allowed * Active or recent hemoptysis (\>= ½ teaspoon of bright red blood per episode) =\< 30 days prior to registration * Serious, non-healing wound, active ulcer, or untreated bone fracture; NOTE: patients with fractures secondary to metastatic disease are eligible after appropriate radiotherapy * Significant vascular disease (e.g., aortic aneurysm, aortic dissection), recent peripheral arterial thrombosis, symptomatic peripheral vascular disease =\< 6 months prior to registration * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess =\< 6 months prior to registration * Major surgical procedures, open biopsy, or significant traumatic injury =\< 28 days prior to registration or anticipation of need for major surgical procedure during the course of the study; EXCEPTION: core biopsy or minor surgical procedure, including placement of a vascular access device, =\< 7 days prior to registration is allowed * Patients taking cytochrome P450 enzyme-inducing antiepileptic drugs =\< 4 weeks prior to registration will be excluded (phenytoin, carbamazepine, phenobarbital, rifampin, or St. John's wort) * Known or suspected allergy or hypersensitivity to any agent given in the course of this trial * Any condition that impairs patient's ability to swallow whole pills * Any malabsorption problem * Any of the following prior therapies: * Chemotherapy =\< 14 days prior to registration * Immunotherapy =\< 28 days prior to registration * Radiation therapy =\< 28 days prior to registration * Radiation to \> 25% of bone marrow * Failure to fully recover from acute, reversible effects of prior chemotherapy regardless of interval since last treatment * Known brain metastasis; NOTE: patients with neurological symptoms must undergo a computed tomography (CT) scan/magnetic resonance imaging (MRI) of the brain to exclude brain metastasis * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\]-approved indication and in the context of a research investigation) * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Other active malignancy =\< 3 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: if there is a history of prior malignancy, they must not be receiving other specific treatment for their cancer, including hormonal therapy