This phase I/II trial studies the side effects and best dose of vorinostat in preventing graft versus host disease in children, adolescents, and young adults who are undergoing unrelated donor blood and bone marrow transplant. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells, called graft-versus-host disease. During this process, chemicals (called cytokines) are released that may damage certain body tissues, including the gut, liver and skin. Vorinostat may be an effective treatment for graft-versus-host disease caused by a bone marrow transplant.