Sorafenib in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia, Acute Lymphoblastic Leukemia, or Chronic Myelogenous Leukemia

Inclusion Criteria: * Patients must have pathological confirmation (histologically or cytologically) of relapsed or refractory acute myeloid leukemia (other than acute promyelocytic leukemia), acute lymphocytic leukemia, or chronic myeloid leukemia in blast crisis * The morphologic diagnosis of AML (non-APL), ALL, and CML in blast crisis will be made independently by members of the hematologic pathology division; routine staining and standard criteria as outlined by the Report of the NCI-Sponsored Workshop will be followed * All patients must have been refractory to or relapsed from their most recent therapy AND are considered ineligible for potential curative approaches including allogeneic stem cell transplant; in addition, patients must be at least: * 3 weeks from last cytotoxic chemotherapy (excluding hydroxyurea) * Hydroxyurea may be used for blast count control but must be discontinued within 48 hours of the initiation of BAY 43-9006 * 2 weeks from last radiation therapy * 3 week from last biologic therapy (including myeloid growth factors) * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 2 months * Multilineage bone marrow failure due to the subject's underlying leukemia * Total blast count in the peripheral blood \< 30,000 * Total bilirubin =\< 2 mg/dl * AST(SGOT)/ALT(SGPT) =\< 5 X institutional upper limit of normal * Serum creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * All 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; the effects of BAY 43-9006 on the developing human fetus at the recommended therapeutic dose are unknown; however, kinase inhibitors are known to be teratogenic; 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 with APL are not eligible for this clinical trial * Patients who have not recovered from adverse events due to agents administered more than 3 weeks earlier * Patients with rapidly increasing peripheral blood blast counts (increase in the absolute peripheral blast count \> 50% within one week) or uncontrolled (absolute blast count \> 30,000) while on hydroxyurea will be excluded * Patients with uncontrolled hypertension (i.e., persistent grade 3 while undergoing treatment) * Patients may not be actively receiving any other investigational agents * Patients active and / or untreated CNS leukemia will not be eligible * History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 * Pregnant women are excluded from this study; 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 * Uncontrolled intercurrent illness including, but not limited to, 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 * Patients must not have any evidence of bleeding diathesis * Patients must not be on therapeutic anticoagulation; prophylactic anticoagulation (i.e. low dose warfarin) of venous or arterial access devices is allowed provided that the requirements for PT, INR or PTT are met * Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or phenobarbital), rifampin or St. John's wort