Additional Study Information: This randomized phase II/III trial studies how well radiation therapy works with durvalumab or cetuximab in treating patients with stage III-IVB head and neck cancer who cannot take cisplatin. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Monoclonal antibodies, such as durvalumab and cetuximab, may interfere with the ability of tumor cells to grow and spread. It is not known if radiation therapy with durvalumab will work better than the usual therapy of radiation therapy with cetuximab in treating patients with head and neck cancer.