Sorafenib and Temsirolimus in Treating Patients With Unresectable or Metastatic Solid Tumors

Inclusion Criteria: * Patients must have histologically confirmed solid malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * ECOG performance status =\< (Karnofsky \>= 60%) * Predicted life expectancy of greater than 12 weeks * Leukocytes \>= 3,000 mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 9.0 g/dL * Platelets \>= 100,000/mcL * Fasting serum cholesterol =\< 350 mg/dL (9.0 mmol/L) * Total bilirubin within normal institutional limits * AST (SGOT)/ALT (SGPT) =\< 2.5 x institutional upper limit of normal (ULN) * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients on prophylactic anticoagulation therapy (e.g., low-dose warfarin) are eligible provided their coagulation parameter levels are as follows: INR (International Normalized Ratio of prothrombin time) \< 1.1 x ULN * Patients on full-dose anticoagulants (e.g., warfarin) with PT INR \> 1.5 are eligible provided that both of the following criteria are met: * The patient has an in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin * The patient has no active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices) * Eligibility of patients receiving any other medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of BAY 43-9006 or CCI-779 will be determined following review of individual cases by the Principal Investigator; patients cannot be receiving enzyme-inducing antiepileptic drugs (EIAEDs) such as phenytoin, phenobarbital, carbamazepine, rifampin, or St. John's wort; patients must avoid grapefruit and grapefruit juice * 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 * Complete supportive and palliative care will continue to be provided to ameliorate signs and symptoms that were pre-existing or may arise while on study and which do not interfere with the objectives of the study; the use of erythropoietin and bisphosphonates is permitted * Patients with CNS metastases are eligible for enrollment if they have received prior treatment (including radiation therapy, stereotactic radiosurgery, surgical resection) to site(s) of CNS metastatic disease, have no requirement for glucocorticoids, are not taking anticonvulsants, and have no overt evidence of neurological deficit; in addition, radiologic scans performed within \< 14 days of study entry should not show evidence of disease progression or peritumoral edema Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events to =\< grade 1 due to agents administered more than 4 weeks earlier, excluding alopecia * Patients who have received any investigational compound within the past 28 days; patients may not be receiving any other investigational agents while participating in the study * History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 or CCI-779 * Hypertension with systolic blood pressure of \> 140 mmHg or diastolic pressure \> 90 mmHg; however, patients with well-controlled hypertension are eligible * Patients must not have any evidence of bleeding diathesis or coagulopathy; patients with PT INR \> 1.5 are excluded, unless the patient is on full dose warfarin * Patients with any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for IV alimentation, prior surgical procedures affecting absorption, or active peptic ulcer disease) that impairs their ability to swallow pills are excluded * Uncontrolled intercurrent illness including, but not limited to, uncontrolled hypertension, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with either of these agents * HIV-positive patients on combination antiretroviral therapy are ineligible * Patients undergoing major surgery or sustaining a significant traumatic injury within 21 days prior to treatment are ineligible