Azacitidine With or Without Entinostat in Treating Patients With Myelodysplastic Syndromes, Chronic Myelomonocytic Leukemia, or Acute Myeloid Leukemia

Inclusion Criteria: * The following diagnoses will be eligible for this study: * Myelodysplastic syndromes: the diagnosis of MDS must be confirmed by a bone marrow aspirate and/or biopsy within two weeks prior to registration; NOTE: blast count must be \< 20%; patients with any International Prognostic Score (IPSS) are eligible; patients with low or intermediate (INT)-1 IPSS must have a platelet count \< 50,000/mm\^3 and/or absolute neutrophil count (ANC) \< 500/mm\^3 within seven days prior to registration * Chronic myelomonocytic leukemia (dysplastic subtype): the diagnosis of CMMoL must be confirmed by a bone marrow aspirate and/or biopsy within two weeks prior to registration; patients with CMMoL must have a WBC \< 12,000/mm\^3, documented within 4 weeks prior to study entry (two sets of counts that are 2 weeks apart will be taken) * Acute myeloid leukemia with multilineage dysplasia: the diagnosis of AML-TLD must be confirmed by a bone marrow aspirate and/or biopsy within two weeks prior to registration; NOTE: there must be evidence of \>= 20% blasts on the review of the bone marrow aspirate and/or biopsy; AML-TLD will be interpreted to include patients formerly diagnosed by French-American-British (FAB) criteria as refractory anemia with excess blasts in transformation (RAEB-t), as well as patients with no history of antecedent hematologic disorder who have AML which meets criteria for AML-TLD by World Health Organization (WHO) criteria; patients with AML-TLD must have…