Sorafenib Tosylate and Bevacizumab in Treating Patients With Advanced Kidney Cancer

Inclusion Criteria: * PHASE I ELIGIBILITY CRITERIA * Patients must have histological or cytological confirmation of renal cell carcinoma (clear cell, papillary, chromophobe, or sarcomatoid) not curable by standard approaches; tumor must be measurable by Response Evaluation Criteria In Solid Tumors (RECIST) criteria; nephrectomy prior to enrollment is not required * Patients may not have had prior therapy with inhibitors of the mitogen-activated protein (MAP) kinase pathway or inhibitors of VEGF and/or its receptor signaling (VEGFR2) * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy of greater than 3 months * Hemoglobin (Hgb) \>= 9.0gm/dl (transfusions allowed prior to enrollment) * White Blood Count \>= 3,000/mm\^3 * Absolute Granulocyte Count \>= 1,200/mm\^3 * Platelet Count \>= 100,000/mm\^3 * Serum creatinine =\< 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) \>= 40ml/min (neither drug is cleared by the kidney) * Total Bilirubin =\< 1.5 x ULN * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x ULN * International normalized ratio (INR) =\< 1.5 and activated partial thromboplastin time (aPTT) that is not greater than 1.3 times the ULN * Urine Dipstick must show less then 1+ protein in urine or the patient will require 24 hour urine collection with total protein =\< 1000 mg/24 hour * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * PHASE II ELIGIBILITY CRITERIA * Patients enrolled on the phase II portion of the study will be required to have predominantly clear cell variant of renal cell carcinoma with less than 25% of any other histology (papillary or chromophobe or oncocytic); there must be histologic confirmation by treating center of either primary or metastatic lesion; patients must be willing to consent for obtaining tumor tissue blocks or unstained slides from prior biopsy or surgery; patients who participated in the Phase I part of the protocol will not be part of the accrual to the Phase II cohort * Patients enrolled on the phase II portion of the study will be required to have measurable disseminated disease that is not curable by standard radiation therapy or surgery * Previous nephrectomy is required with the following exceptions: * Primary tumor =\< 5cm or * Extensive liver (\> 30% of liver parenchymal) or multiple (\> 5) bone metastases, or extensive extrarenal tumor or unresectable local/regional tumor extension making nephrectomy a clinically questionable and unreasonable procedure * For the phase II study, patients will be allowed no more than one prior regimen containing a vaccine or cytokine based immunotherapy or chemotherapy for advanced disease * Hgb \>= 9.0gm/dl (transfusions allowed prior to enrollment) * White Blood Count \>= 3,000/mm\^3 (phase II) * Absolute Granulocyte Count \>= 1,200/mm\^3 (phase II) * Platelet Count \>= 100,000/mm\^3 (phase II) * Serum creatinine =\< 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) \>= 40ml/min (neither drug is cleared by the kidney) (phase II) * Total Bilirubin =\< 1.5 x ULN (phase II) * AST/ALT =\< 2.5 x ULN * INR =\< 1.5 * Urine Dipstick must show less then 1+ protein in urine or the patient will require 24 hour urine collection with total protein =\< 1000 mg/24 hour (phase II) * No prior malignancy diagnosed within the past 3 years with the exception of non-melanoma skin cancers, melanoma in situ, carcinoma in situ of the cervix, ductal carcinoma in situ, and lobular carcinoma in situ; any prior malignancy must have a very likely cure rate (75% or greater) * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant while participating in this study, she should inform her treating physician immediately (phase II) * Ability to understand and the willingness to sign a written informed consent document (phase II) Exclusion Criteria: * History or clinical evidence of central nervous system (CNS) disease, including primary brain tumor (participants with a history of meningioma are not excluded), seizures not controlled with standard medical therapy, any brain metastasis, or history of stroke within the prior 12 months; patients who have had a history of brain metastasis that have been resected or have had radiosurgery with no progression for more than 6 months are eligible if the Principle Investigator from the coordinating center is consulted and agrees * Patients entered onto the phase II study may not have received more than one chemotherapy or immunotherapy regimen for Stage IV disease * Patients may not have received chemotherapy or immunotherapy within 4 weeks of initiating treatment; patients will not have received a regimen containing a monoclonal antibody within 8 weeks of initiating treatment; toxicities from radiation must have resolved and a minimum of two weeks must pass prior to enrollment * Patients may not have had prior anti-angiogenic therapy including, Sunitinib, VEGF Trap; prior Temsirilomus, Everolimus, Bevacizumab and Sorafenib will not be allowed; thalidomide or interferon (IFN) alpha are allowed either for adjuvant therapy or stage IV disease * History of allergic reactions attributed to Chinese hamster ovary cell products, other recombinant human antibodies, or compounds of similar chemical or biologic composition to Sorafenib * History of bleeding diathesis or coagulopathy * A condition that impairs patient's ability to swallow pills will make patient ineligible * No major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to initiation of therapy on trial * Anticipation of the need for major surgery during the course of the study * Current or recent use (within 7 days of starting the study drugs) of full-dose of anticoagulants (except as required to maintain patency of preexisting, permanent indwelling IV catheters or for deep vein thrombosis \[DVT\] prophylaxis, for subjects receiving warfarin, INR should be =\< 1.5) or thrombolytic agent * Patients with uncontrolled hypertension; blood pressure must be =\< 150/90 mmHg at the time of enrollment on a stable antihypertensive regimen * Patients with clinically significant cardiovascular disease within 1 year prior to study entry * Uncontrolled hypertension * Myocardial infarction or unstable angina \< 6 months prior to registration * New York heart association grade II or greater congestive heart failure, serious cardiac arrhythmia requiring medication (participants with controlled atrial arrhythmias are not excluded), unstable angina pectoris * Grade II or greater peripheral vascular disease * Serious, non-healing wound, ulcer, or bone fracture * Significant proteinuria (\> 1000 mg protein/24 hours ) at baseline; subjects discovered to have \>= 1+ proteinuria on dipstick should undergo a 24-hour urine collection, which should contain \< 1000 mg protein/ 24 hours to be allowed participation in the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection requiring parental antibiotics, or psychiatric illness/social situations that would limit compliance with study requirements * Patients taking cytochrome P450 enzyme-inducing antiepileptic drugs will be excluded (phenytoin, carbamazepine, Phenobarbital, rifampin, and St.John's Wort) * Pregnant and lactating women are excluded from the study; breastfeeding should be discontinued while receiving therapy * Human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study