Sorafenib in Treating Patients With Refractory or Relapsed Acute Leukemia, Myelodysplastic Syndromes, or Blastic Phase Chronic Myelogenous Leukemia

Inclusion Criteria: Diagnosis of 1 of the following: Acute myeloid leukemia (Acute promyelocytic leukemia (M3) allowed provided patient has failed prior therapy with both tretinoin and arsenic alone or in combination); Acute lymphoblastic leukemia; Myelodysplastic syndromes; Blastic phase chronic myelogenous leukemia (Failed OR intolerant to imatinib mesylate) Must have failed prior therapy with >= 1 cytotoxic- or biologic-targeted agent (e.g., hypomethylating agents, farnesyl transferase inhibitors, thalidomide, or tyrosine kinase inhibitors); Any number of prior regimens allowed Performance status: ECOG 0-1 ALT =< 2.5 times upper limit of normal Bilirubin =< 1.5 mg/dL Creatinine =< 2.0 mg/dL OR Creatinine clearance >= 60 mL/min Fertile patients must use effective contraception No psychiatric illness or social situation that would preclude study compliance Prior bone marrow transplantation allowed At least 2 weeks since prior cytotoxic agents OR at least 5 half-lives for non-cytotoxic agents in the absence of rapidly progressing disease At least 24 hours since prior hydrea for control of peripheral blood leukemia cell counts Hydroxyurea allowed up to 72 hours after start of therapy with sorafenib No persistent, chronic, clinically significant toxicities > grade 1 from prior chemotherapy Exclusion Criteria: Cytopenias secondary to multilineage bone marrow failure allowed Ineligible for or not willing to undergo allogeneic stem cell transplantation OR no donor available Absolute blast count=< 20,000/mm^3 unless patient has documented fms-like tyrosine kinase 3 internal tandem duplication No evidence of bleeding diathesis (except due to low platelets associated with the primary disease) No New York Heart Association class III or IV congestive heart failure No uncontrolled hypertension (i.e., sustained systolic blood pressure [BP] >= 150 mm Hg or diastolic BP >= 90 mm Hg) No unstable angina pectoris No symptomatic cardiac arrhythmia requiring and not responding to medical intervention Not pregnant or nursing No history of allergic reaction attributed to compounds of similar chemical or biological composition to the study drug No swallowing dysfunction that would impede oral ingestion of tablets No active uncontrolled infection No other uncontrolled illness No prior sorafenib No other concurrent investigational or commercial agents, except for standard intrathecal chemotherapy for the treatment of isolated CNS leukemic involvement No other concurrent anticancer agents No concurrent combination antiretroviral therapy for HIV-positive patients No concurrent therapeutic anticoagulation (Concurrent prophylactic anticoagulation [i.e., low-dose warfarin, catheter flushing with heparin] of venous or arterial access devices allowed) No concurrent cytochrome P450 enzyme-inducing antiepileptic agents, including, but not limited to, any of the following: Phenytoin; Carbamazepine; Phenobarbital; Rifampin No concurrent Hypericum perforatum (St. John's wort)