MS-275 and Azacitidine in Treating Patients With Myelodysplastic Syndromes, Chronic Myelomonocytic Leukemia, or Acute Myeloid Leukemia

Inclusion Criteria: * Diagnosis of 1 of the following: * Histologically confirmed myelodysplastic syndromes (MDS) by bone marrow aspiration and/or biopsy * International Prognostic Scoring System (IPSS) score of intermediate-1, intermediate-2, or high * International Prognostic Scoring System (IPSS) score of intermediate-1, intermediate-2, or high * Low IPSS score allowed provided patient has a clinically significant cytopenia (i.e., absolute neutrophil count \< 1,000/mm\^3, untransfused hemoglobin \< 8 g/dL, platelet count \< 20,000/mm\^3, or anemia requiring transfusion) * Chronic myelomonocytic leukemia * Acute myeloid leukemia (AML) * Relapsed or refractory disease * Untreated AML allowed provided patient meets \>= 1 of the following criteria: * Age 60 and over * AML arising in the setting of an antecedent hematologic disorder * High-risk cytogenetic abnormalities * Medical conditions that may compromise the ability to give cytotoxic chemotherapy as the primary modality * Refused cytotoxic chemotherapy * WBC \< 30,000/mm3 for \>= 2 weeks before study entry * Acute promyelocytic leukemia allowed provided patient is in at least second relapse and has already received treatment regimens containing arsenic trioxide and isotretinoin * No clinical evidence of CNS or pulmonary leukostasis or CNS leukemia * Peformance status: * Zubrod 0-2 * Life expectancy: * At least 6 months * Hematopoietic: * See Disease Characteristics * Hemoglobin ≥ 8 g/dL (transfusion allowed) * No disseminated intravascular coagulation * Renal: * Creatinine normal OR * Creatinine clearance \>= 60 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for 3 months after study treatment * No untreated, active infection * No other serious or uncontrolled medical condition * More than 3 weeks since prior hematopoietic growth factors for this malignancy * At least 3 weeks since prior hydroxyurea (2 weeks for AML patients) * No concurrent hydroxyurea * Recovered from all prior therapy * At least 2 weeks since prior cytotoxic therapy (AML patients) * More than 3 weeks since other prior therapy for this malignancy * No other concurrent investigational or commercial agents or therapies for this malignancy * No concurrent valproic acid * Hepatic: * Bilirubin normal unless due to hemolysis or Gilbert's syndrome * AST and ALT =\< 2.5 times upper limit of normal