This phase I trial studies the side effects and best dose and schedule of sirolimus when given together with vaccine therapy in treating patients with stage II-IV ovarian epithelial, fallopian tube, or primary peritoneal cavity cancer. Sirolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Vaccines made from a gene-modified virus may help the body build an effective immune response to kill tumor cells. Giving vaccine therapy together with sirolimus may be an effective treatment for ovarian, fallopian tube, or primary peritoneal cancer