I. To select based on response rate (complete remission, partial remission, or hematologic improvement) either the combination of lenalidomide and azacitidine or the combination of vorinostat and azacitidine for further testing against single-agent azacitidine among patients with higher-risk myelodysplastic syndromes (MDS) or chronic myelomonocytic leukemia (CMML). (Phase II) II. To compare overall survival between the combination arm selected in the Phase II portion of the trial to single-agent azacitidine among patients with higher-risk myelodysplastic syndromes (MDS) or chronic myelomonocytic leukemia (CMML). (Phase III)