This partially randomized phase I/IIb trial studies the side effects and best dose of IDO1 inhibitor INCB024360 in combination with DEC-205/NY-ESO-1 fusion protein CDX-1401 and poly ICLC and to see how well they work in treating patients with ovarian, fallopian tube, or primary peritoneal cancer who no longer have evidence of disease. Antigens (such as cancer/testis antigen [NY-ESO-1] protein) are found on many cancer cells. Vaccines made from NY-ESO-1 protein may cause the immune system to produce immune cells and antibodies that may help locate the NY-ESO-1 and/or cancer/testis antigen 2 (LAGE-1) antigens on cancer cells. By finding them, the immune system may then work to control or eliminate the remaining cancer cells. INCB024360 is an inhibitor of an enzyme called indoleamine 2,3 dioxygenase (IDO). This enzyme is produced by tumor cells to disable immune cells, and limit the efficacy of immune attack. Giving DEC-205/NY-ESO-1 fusion protein CDX-1401 with poly ICLC and IDO1 inhibitor INCB024360 may generate stronger and more long lasting anti-cancer immune responses in patients with ovarian, fallopian tube, and primary peritoneal cancer in remission.