This randomized phase II/III trial studies how well cediranib maleate and olaparib work when given together or separately, and compares them to standard chemotherapy in treating patients with ovarian, fallopian tube, or primary peritoneal cancer that has returned after receiving chemotherapy with drugs that contain platinum (platinum-resistant) or continued to grow while being treated with platinum-based chemotherapy drugs (platinum-refractory). Cediranib maleate and olaparib may stop the growth of tumor cells by blocking enzymes needed for cell growth. Drugs used in chemotherapy work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known whether giving cediranib maleate and olaparib together may cause more damage to cancer cells when compared to either drug alone or standard chemotherapy.