Sorafenib, Gemcitabine, and Capecitabine in Treating Patients With Unresectable and/or Metastatic Kidney Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed renal cell carcinoma that is unresectable and/or metastatic; patients with collecting duct carcinoma, oncocytomas, or transitional cell carcinoma are not eligible; patients with sarcomatoid renal cell carcinoma are eligible, but those with pure sarcomas are not; histologic documentation of metastatic disease is not required; clinical confirmation, but not pathologic staging, of metastatic disease is required * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan * Patients may have received one prior immunotherapy based regimen (i.e. interleukin-2 or interferon alpha) ending \>= 4 weeks prior to enrollment * Patients may have received up to 2 prior regimens containing mitogen-activated protein kinases (MAPK), vascular endothelial growth factor (VEGF) pathway inhibitors (e.g. sunitinib or bevacizumab) and/or mammalian target of rapamycin (mTOR) inhibitor (e.g. temsirolimus) ending \>= 4 weeks prior to enrollment * Life expectancy of more than 3 months * Eastern Cooperative Oncology Group (ECOG) =\< 2 OR Karnofsky \>= 60% * Leukocytes \>= 3000/uL * Absolute neutrophil count \>= 1,500/uL * Platelet count \>= 100,000/uL * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase \[SGPT\]) =\< 2.5 x IULN * Creatinine =\< 1.5 x IULN OR creatinine clearance \>= 60 mL/min/1.73m\^2 for patients with creatinine levels above institutional normal * The effects of sorafenib on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because raf kinase inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, 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 or suspect she is 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 Exclusion Criteria: * Patients may not have received prior chemotherapy; if patients have had prior definitive or other surgery, prior radiation therapy, they must have fully recovered from the effects of therapy with at least 4 weeks recovery time; for patients who have had a surgical biopsy only, they must have simply recovered * Patients may not be receiving any other investigational agents * Patients with known active brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; previously treated brain metastases are allowed if they show no evidence of progression on CT or magnetic resonance imaging (MRI) at least 8 weeks after completion of surgery and/or radiotherapy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib, gemcitabine and capecitabine * No concurrent megestrol is permitted; no megestrol therapy within 4 weeks prior to protocol treatment is allowed; no concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, phenobarbitol or carbamazepine), rifampin, or St. John's wort * Uncontrolled intercurrent illness including, but not limited to, uncontrolled hypertension, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, pulmonary disease including asthma, chronic bronchitis, emphysema with requirements for chronic oxygen use or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because sorafenib 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 sorafenib, breastfeeding should be discontinued if the mother is treated with sorafenib; the potential risks may apply to other agents used in this study * Because patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy, human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with sorafenib, gemcitabine, or capecitabine administered during the study; appropriate studies will be undertaken in patients receiving combination ant-retroviral therapy when indicated * Any swallowing dysfunction leading to difficulty taking the investigational therapy or capecitabine * Prior treatment with sorafenib * Patients with any history or evidence of a bleeding diathesis * Patients on therapeutic anticoagulation with coumarins (e.g. warfarin); prophylactic coumarin-based anticoagulation (i.e. low dose warfarin) for venous or arterial access devices is allowed provided that the requirements for prothrombin time (PT), international normalization ratio (INR) and/or partial thromboplastin time (PTT) are met; prophylactic or therapeutic low molecular weight heparin is allowed; patients with known brain metastases are excluded (even if treated and stable) if they are also on therapeutic doses of anticoagulation * Patients with known dihydropyrimidine dehydrogenase deficiency