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 a white blood cell
   (WBC) =< 30,000/mm^3 documented within 4 weeks prior to study entry (two sets of
   counts that are 2 weeks apart will be taken); patients whose WBC has doubled within
   this period of time and is greater than 20,000/mm^3 at the time of screening will not
   be eligible

   - Women must not be pregnant or breast-feeding; all females of childbearing potential
   must have a blood test or urine study within two weeks prior to registration to rule
   out pregnancy

   - Women of childbearing potential and sexually active males must be strongly advised to
   use an accepted and effective method of contraception

   - Patient must have Eastern Cooperative Oncology Group (ECOG) performance status between
   0-2

   - Patient must have no prior treatment with azacitidine, decitabine or entinostat

   - Patients must not have active infections at the time of registration

   - Serum creatinine < 2.0 mg/dL; test must be done within seven days prior to
   registration

   - Total serum bilirubin within institutional limits unless due to intra- or
   extramedullary hemolysis or Gilbert's syndrome; test must be done within seven days
   prior to registration

   - Aspartate transaminase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
   alanine transaminase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x
   institutional upper limit of normal (ULN); tests must be done within seven days prior
   to registration

   - Patients must not have received any AML induction chemotherapy or stem cell
   transplantation; any other treatment for their disease, including hematopoietic growth
   factors may not be given, within three weeks prior to registration, and should have
   recovered from all toxicities of prior therapy (to grade 0 or 1)

   - Patients must have no clinical evidence of central nervous system (CNS) or pulmonary
   leukostasis, disseminated intravascular coagulation, or CNS leukemia

   - Patients must have no serious or uncontrolled medical conditions

   - Patients who have therapy-induced MDS, CMMoL (dysplastic) and AML-TLD are eligible and
   will be treated as separate cohorts from the patients with de novo MDS, CMMoL
   (dysplastic) and AML-TLD

   - Patients should have a life expectancy of at least six months

   - Patients must not have advanced malignant hepatic tumors

   - Patients must not have a known hypersensitivity to azacitidine or mannitol

   - Southwest Oncology Group (SWOG) ONLY: all SWOG patients must be registered on
   SWOG-9007 ("Cytogenetic Studies in Leukemia Patients"); collection of the pretreatment
   bone marrow specimen (or of peripheral blood if the marrow is not aspirable) must be
   completed within 28 days before registration; the pretreatment specimen must be
   submitted to a SWOG-approved cytogenetics laboratory as described in protocol
   SWOG-9007; note that submission of bone marrow cytogenetic studies are required to
   calculate the IPSS score (stratification issue); in addition, cytogenetic response
   will be measured at follow-up requiring a second cytogenetic study at the end of
   protocol treatment; NOTE: In addition to SWOG-9007, SWOG patients must be offered
   participation in S9910, the leukemia centralized reference laboratories and tissue
   repositories ancillary study; If consent is given, collection of pretreatment blood
   and/or marrow specimens must be completed within 14 days prior to registration. If the
   patient consents to participate in S9910, pretreatment specimens of marrow and/or
   peripheral blood must be submitted to the Southwest Oncology Group Myeloid Repository
   at the University of New Mexico for cellular and molecular studies; S9910 also
   requests submission of remission and relapse specimens