This randomized phase II/III trial studies how well azacitidine works with or without lenalidomide or vorinostat in treating patients with higher-risk myelodysplastic syndromes or chronic myelomonocytic leukemia. Drugs used in chemotherapy, such as azacitidine, work in different ways to stop the growth of cancer cells, either by killing the cells, stopping them from dividing, or by stopping them from spreading. Lenalidomide may stop the growth of cancer cells by stopping blood flow to the cancer. Vorinostat may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. It is not yet known whether azacitidine is more effective with or without lenalidomide or vorinostat in treating myelodysplastic syndromes or chronic myelomonocytic leukemia.