This phase III trial compares the effect of adding immunotherapy (brentuximab vedotin and nivolumab) to standard treatment (chemotherapy with or without radiation) to the standard treatment alone in improving survival in patients with stage I and II classical Hodgkin lymphoma. Brentuximab vedotin is in a class of medications called antibody-drug conjugates. It is made of a monoclonal antibody called brentuximab that is linked to a cytotoxic agent called vedotin. Brentuximab attaches to CD30 positive lymphoma cells in a targeted way and delivers vedotin to kill them. A monoclonal antibody is a type of protein that can bind to certain targets in the body, such as molecules that cause the body to make an immune response (antigens). Immunotherapy with monoclonal antibodies, such as nivolumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs such as doxorubicin hydrochloride, bleomycin sulfate, vinblastine sulfate, dacarbazine, and procarbazine hydrochloride work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Cyclophosphamide is in a class of medications called alkylating agents. It works by damaging the cell's deoxyribonucleic acid (DNA) and may kill cancer cells. It may also lower the body's immune response. Etoposide is in a class of medications known as podophyllotoxin derivatives. It blocks a certain enzyme needed for cell division and DNA repair and may kill cancer cells. Vincristine is in a class of medications called vinca alkaloids. It works by stopping cancer cells from growing and dividing and may kill them. Prednisone is in a class of medications called corticosteroids. It is used to reduce inflammation and lower the body's immune response to help lessen the side effects of chemotherapy drugs. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Adding immunotherapy to the standard treatment of chemotherapy with or without radiation may increase survival and/or fewer short-term or long-term side effects in patients with classical Hodgkin lymphoma compared to the standard treatment alone.