Sorafenib Tosylate With or Without Recombinant Interferon Alfa-2b in Treating Patients With Metastatic Kidney Cancer

Inclusion Criteria: * Patients with histologically or cytologically confirmed metastatic clear cell RCC * Patients must have measurable disease, defined as a lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) and measures \>= 20 mm with conventional techniques or \>= 10 mm with spiral CT scan * ECOG performance status =\< 1 * Absolute neutrophil count \>= 1,500/μL * Platelets \>= 100,000/μL * Hgb \> 9.0 g/dL (may be transfused or receive epoetin alfa \[e.g., Epogen®\] to maintain or exceed this level) * Total bilirubin =\< 2.0 mg/dl * Albumin \> 3.0 g/dL * Serum creatinine =\< 2.0 mg/dl * AST(SGOT) and/or ALT (SGPT) =\< 2.5 X institutional upper limit of normal for subjects without evidence of liver metastases * AST(SGOT) and/or ALT (SGPT) =\< 5 X institutional upper limit of normal for subjects with documented liver metastases * Female patients of childbearing potential must have a normal plasma beta human chorionic gonadotropin (βHCG) within 24 hours prior to enrolling in the study due to the possible teratogenic effect; however, patients will be eligible if their βHCG elevation is consistent with malignancy rather than pregnancy * Patients of child fathering or childbearing potential must agree to practice a form of medically acceptable birth control while on study * Patients must give written informed consent prior to initiation of therapy, in keeping with the policies of the institution; patients with a history of major psychiatric illness must be judged able to fully understand the investigational nature of the study and the risks associated with the therapy; the only approved consent is attached to this protocol * Patients must have ability to comply with study and/or follow-up procedures * Patients must be able to swallow pills Exclusion Criteria: * No prior malignancy is allowed, except for non-melanoma skin cancer, in situ carcinoma of any site, or other cancers for which the patient has been adequately treated and disease free for 5 years * Patients must not have received any systemic anticancer therapy for renal cell carcinoma; patients must not have received any radiotherapy for renal cell carcinoma within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients must not be scheduled to receive another experimental drug while on this study; patients are permitted to be on concomitant bisphosphonates * Patients must not have a primary brain tumor, any brain metastases, leptomeningeal disease, seizure disorders not controlled with standard medical therapy, or history of stroke * Patients must not have active acute infections that could be worsened by anticancer therapy or interfere with this study * Patients must not have clinically significant cardiovascular disease, myocardial infarction within the past year (unstable angina), New York Heart Association (NYHA) Grade II or greater congestive heart failure, serious cardiac dysrhythmia refractory to medical management, or peripheral vascular disease (Grade II or greater) * Patients must not have uncontrolled hypertension * Patients must not have history of other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that might affect the interpretation of the results of the study or render the subject at high risk from treatment complications * Pregnant women are excluded from this study because BAY 43-9006 is a kinase inhibitor agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with BAY 43-9006, breastfeeding should be discontinued if the mother is treated with BAY 43-9006 * Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with BAY 43-9006; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated * Patients must not have a clinical history of coagulopathy, bleeding diathesis or thrombosis; patients must not be on therapeutic anticoagulation; prophylactic anticoagulation (ie low dose warfarin) of venous access devices is allowed provided that INR \>= 1.5 is due to warfarin therapy; other patients with an INR \>= 1.5 are excluded * Patients must not have a history of severe depression * Concomitant treatment with rifampin, St. John's wort, and the cytochrome p450 enzyme-inducin antiepileptic drugs (phenytoin, carbamazepine or Phenobarbital)