This phase II trial studies the possible benefits of treatment with different combinations of the drugs durvalumab, olaparib and cediranib vs. the usual treatment in patients with ovarian, primary peritoneal, or fallopian tube cancer that has come back after a period of improvement with platinum therapy (recurrent platinum resistant). Usual treatment is the type of treatment most patients with this condition receive if they are not part of a clinical study. Combination therapies studied in this trial include MEDI4736 (durvalumab) plus olaparib and cediranib, durvalumab and cediranib, or olaparib and cediranib. Monoclonal antibodies, such as durvalumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumors cells to grow and spread. Olaparib is an inhibitor of PARP, an enzyme that helps repair deoxyribonucleic acid (DNA) when it becomes damaged. Blocking PARP may help keep cancer cells from repairing their damaged DNA, causing them to die. PARP inhibitors are a type of targeted therapy. Cediranib may stop the growth of tumor cells by blocking VEGF (an enzyme). needed for cell growth. Giving different combinations of durvalumab, olaparib and cediranib may work better in increasing the duration of time that the cancer does not progress compared to the usual treatment.