Testing the Combination of New Anti-cancer Drug Peposertib With Avelumab and Radiation Therapy for Advanced/Metastatic Solid Tumors and Hepatobiliary Malignancies

Inclusion Criteria: * PHASE 1: Patients must have a histologically confirmed metastatic or locally advanced unresectable solid tumor that has progressed on or after available standard of care therapy or for which no acceptable standard of care therapy exists, or in which the patient declines standard of care therapy (each patient that declines standard of care therapy will be documented in the case report form) * PHASE 2: Patients must have a histologically confirmed metastatic or locally advanced unresectable cholangiocarcinoma/gallbladder carcinoma that has progressed on gemcitabine, cisplatin, and durvalumab/pembrolizumab * Age \>= 18 years * Because no dosing or adverse event data are currently available on the use of peposertib (M3814) in combination with avelumab in patients \< 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Patients with at least 1 index lesion to irradiate for whom palliative radiation treatment is indicated (including but not limited to pain and/or symptom control, prevention of disease -related complications, and preservation of organ function). Lung and liver lesions are preferred, though alternate lesions may be considered after discussion with trial principal investigator (PI). Up to 2 lesions may be considered for irradiation provided at least 1 lesion will receive the study treatment of total of 60 Gy and all prescribed irradiation will be completed within the radiation window * Pat…