This phase I/II trial studies the best dose and side effects of olaparib and how well it works with radium Ra 223 dichloride in treating patients with castration-resistant prostate cancer that has spread to the bone and other places in the body. Olaparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Radioactive drugs, such as radium Ra 223 dichloride, may carry radiation directly to tumor cells and not harm normal cells. Giving olaparib and radium Ra 223 dichloride may work better at treating castration-resistant prostate cancer.