Pemetrexed Disodium and Sorafenib Tosylate in Treating Patients With Advanced Solid Tumors

Inclusion Criteria: * Advanced solid tumor malignancy for which there is no potentially curative treatment; there is no limit to the number of prior lines of therapy * Performance status Eastern Cooperative Oncology Group (ECOG) equal or less than 1 * Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =\< 3 x upper institutional limit (ULN) * Total bilirubin =\< 1.5 ULN * Creatinine clearance (CrCl) \>= 45 mL/min as measured by the standard Cockcroft-Gault equation * International normalized ratio (INR) =\< 1.5 (if not due to anticoagulants) * White blood cell count (WBC) \>= 3,000 cells/mm3 * Absolute neutrophil count (ANC) \>= 1,500 cells/mm3 * Platelets \>= 100,000 cells/mm3 * Hemoglobin (Hgb) \>= 8.5 g/dL * Prior toxicities are allowed as long as they are stable and would not interfere with study drug toxicity assessment * Measurable or evaluable disease by Response Evaluation Criteria In Solid Tumors (RECIST) (v 1.1) * Ability to understand and the willingness to sign a written informed consent document; a signed informed consent must be obtained prior to any study specific procedures * Women of childbearing potential must have a negative pregnancy test performed within 7 days prior to the start of treatment; women of childbearing potential and men must agree to use a medically accepted form of birth control for the duration of study participation; men must agree to use a medically accepted form of birth control for 2 months following completion of study treatment Exclusion Criteria: * Any investigational agent within 4 weeks of first dose of study treatment * Unwillingness or inability to take folic acid, vitamin B12, or dexamethasone * Known or presumed intolerance of pemetrexed or sorafenib; unable to swallow medication; suspected malabsorption * Active illicit substance or alcohol abuse * Contraindication to antiangiogenic agents, including: * Pulmonary hemorrhage/bleeding event \>= Grade 2 within 4 weeks or less prior to the first dose of study drug * Any other hemorrhage/bleeding event \>= Grade 3 within 4 weeks or less prior to the first dose of study drug * Serious non-healing wound, ulcer, or bone fracture * Thrombolic or embolic events such as a myocardial infarction, cerebrovascular accident including transient ischemic attacks within the past 6 months * Major cardiac dysfunction, such as uncontrolled angina, congestive heart failure with New York Heart Association (NYHA) class III or higher, ventricular arrhythmias requiring anti-arrhythmic therapy * Systolic blood pressure \> 160 mmHg or diastolic pressure \> 100 mmHg despite optimal medical management * Inability to interrupt aspirin or other nonsteroidal anti-inflammatory agents for a 5 day period * Serious uncontrolled infection \> Common Terminology Criteria for Adverse Events (CTCAE) (v 4) grade 2 * Peripheral motor or sensory neuropathy\>CTCAE (v4) grade 2 * Uncontrolled metastatic brain disease * Serum B12 or folate levels below the institution's lower limit of normal. Patients may begin B12/folic acid supplementation and can be reconsidered for study once levels meet the eligibility requirements * Administration of non-steroidal anti-inflammatory drugs (NSAIDs) within 5 days prior to pemetrexed dosing (note: if a candidate routinely takes NSAIDs prior to enrollment, consider transition to alternate non-NSAID for duration of study treatment, if possible). * Other condition(s) that in the opinion of the investigator might compromise the objectives of the study