This is a two part, single-institution, open-label, Phase I dose-escalation study of oral 5-azacitidine in combination with intravenous (IV) romidepsin. Part 1 of the study is a traditional 3 + 3 dose escalation study designed to evaluate the maximum tolerated dose (MTD), dose limiting toxicities (DLTs), safety, pharmacokinetic (PK) profiles, and pharmacodynamic profiles of increasing doses of orally administered 5-azacitidine in combination with a constant dose of IV romidepsin. Part 2 is an expansion cohort study for the preliminary evaluation of efficacy in the treatment of virally mediated cancers and liposarcoma once the MTD has been determined. PK and PD data will also be collected for these subjects.