Phase I/II Study of the Anti-Programmed Death Ligand-1 Durvalumab Antibody (MEDI4736) in Combination With Olaparib and/or Cediranib for Advanced Solid Tumors and Advanced or Recurrent Ovarian, Triple Negative Breast, Lung, Prostate and Colorectal Can...

Background: \- Durvalumab is a drug that may help people s immune systems respond to and kill cancer cells. Olaparib is a drug that may inhibit repairing DNA damage of cancer cells. Cediranib is a drug that may stop the blood vessel growth of cancer cells. This study has two components. In the phase 1 component of the study, researchers want to investigate how well participants tolerate the combination of these drugs in treating advanced solid tumors, and in the phase 2 part of this study, researchers want to study if the combination treatments are effective in ovarian cancer. Objectives: \- Phase 2 part of the study: To determine how effective this combination is in treating ovarian cancer. Eligibility: \- Phase 2 part of the study: Adults age 18 or older with advanced or recurrent ovarian cancer that has no standard treatment. Design: * Participants will be screened with medical history, physical exam, and blood and urine tests. They will have CT or MRI scans. For these, they will lie in a machine that takes pictures of their bodies. * Phase 2 part of the study requests the participants to have tumor samples removed. * Participants will get Durvalumab through an IV. A small plastic tube will be inserted into a vein. The drug will be given every 4 weeks until disease progression. * Participants will take olaparib or cediranib by mouth every day. * Every 28 days will be 1 cycle. For cycle 1, participants will have 2 study visits. All other cycles, they will have 1 visit. At these visits, they will repeat the screening procedures. * Patients will keep a drug and diarrhea diary. * Patients on cediranib will monitor their blood pressure and keep a blood pressure diary. * Participants who can become pregnant, or have a partner who can become pregnant, must practice an effective form of birth control. * After 12 cycles, participants will have 1-3 months of follow-up.