DEC-205/NY-ESO-1 Fusion Protein CDX-1401, Poly ICLC, Decitabine, and Nivolumab in Treating Patients With Myelodysplastic Syndrome or Acute Myeloid Leukemia

Inclusion Criteria: * Have a confirmed diagnosis of: * International Prognostic Scoring System (IPSS) intermediate-1, intermediate-2 or high-risk MDS including chronic myelomonocytic leukemia (CMML) OR * Low blast count AML with =\< 30% blasts previously classified as refractory anemia with excess blasts in transformation * Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Hepatic: * Total bilirubin =\< 3 X upper limit of normal (ULN) (except subjects with Gilbert syndrome, who can have total bilirubin up to 3.5 X ULN) * Aspartate aminotransferase (aspartate transaminase \[AST\]/serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (alanine transaminase \[ALT\]/serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 X ULN * Serum creatinine =\< 2.5 X ULN * Troponin-I =\< ULN * Creatine kinase (CK)-MB =\< ULN * Left ventricular ejection fraction (LVEF) \>= ULN (institutional limit) * Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form …