This phase II trial tests how well relugolix and enzalutamide, in combination with radiation therapy, works in treating patients with very high risk prostate cancer. Relugolix is a form of androgen deprivation therapy. It prevents the release of testosterone, a hormone required to sustain prostate growth. Reducing testosterone levels may inhibit the proliferation of prostate tumor cells that need testosterone to grow. Enzalutamide is an androgen receptor signaling inhibitor. It inhibits the activity of prostate tumor cell receptors, which may reduce proliferation of prostate tumor cells. Radiation therapy uses high energy x-rays, particles, or radioactive seeds to kill cancer cells and shrink tumors. Adding relugolix and enzalutamide to radiation therapy may be more effective at treating patients with very high risk prostate cancer than giving any of these treatments alone.