OUTLINE: Beginning at least 3 weeks after completion of cytoreductive combination chemotherapy, patients under age 18 undergo total body irradiation (TBI) twice a day on days -7 to -4. Patients age 18 and over undergo TBI twice a day on days -6 to -4. All patients then receive cyclophosphamide IV daily on days -3 and -2. Males with acute lymphocytic leukemia, high-grade lymphoma, intermediate-grade lymphoma, or marrow or CNS involvement receive radiotherapy boost to the testes. On day 0, patients receive infusion of bone marrow from unrelated donors with 1 of the following: 1 HLA-A or B non-cross-reactive group mismatch; 1 HLA-A or B cross-reactive group mismatch; or an HLA-A, B, and C match with an HLA-DRB1 or DQB1 mismatch.