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 prior to receiving any study related procedure
* No prior exposure to Nivolumab
* No prior investigational therapy within 2 weeks prior to study enrollment

Exclusion Criteria:

* We will exclude patients who are eligible for an allogeneic bone marrow transplant at the time of study enrollment; if an enrolled patient subsequently becomes eligible for transplant, they will not be prevented from proceeding to the appropriate clinical treatment indicated
* Subjects with life-threatening illnesses other than MDS, uncontrolled medical conditions or organ system dysfunction which, in the investigator?s opinion, could compromise the subject?s safety, or put the study outcomes at risk
* AML associated with inv(16); t(16;16); t(8;21) or t(15;17)
* Previously untreated MDS with isolated del5q (for which lenalidomide is approved as approved therapy) and chronic myelomonocytic leukemia (CMML) with rearrangements of the PDGF receptor (for which imatinib is approved therapy) unless they have previously failed these approaches
* Subjects with symptomatic central nervous system (CNS) disease which is not adequately controlled
* Subjects who have received prior radiation therapy for extramedullary disease within 2 weeks of first dose
* Has known immunosuppressive disease (e.g. human immunodeficiency virus \[HIV\], acquired immunodeficiency syndrome \[AIDS\] or other immune depressing disease); testing is not required, only to be done for a possible diagnosis which is not confirmed
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; in addition, subjects will be excluded for any of the following:

  * Myocardial infarction or arterial or venous thromboembolic events within 6 months prior to baseline or severe or unstable angina, New York Heart Association (NYHA) class III or IV disease
  * Active congestive heart failure (New York Heart Association functional classification III or IV)
  * Documented history of cardiomyopathy with EF \< 30%
  * Uncontrolled hypertension (systolic blood pressure \[SBP\] \> 160/diastolic blood pressure \[DBP\] \> 100 despite medical intervention)
  * History of myocarditis of any etiology
* Subjects who have hypersensitivity to decitabine, CDX-1401, poly-ICLC or nivolumab
* History of auto-immune disease (e.g., thyroiditis, lupus), except vitiligo
* Pregnant or nursing female subjects
* Unwilling or unable to follow protocol requirements
* Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug
* Regular use of immunosuppressant drugs such as steroids (\> 20 mg prednisone equivalents), azathioprine, tacrolimus, cyclosporine, etc\>. Use is not permitted within 4 weeks before recruitment