 This phase I trial studies the side effects and best dose of WEE1 inhibitor AZD1775 and belinostat when given together in treating patients with myeloid malignancies that have returned after a period of improvement or have not responded to previous treatment or patients with untreated acute myeloid leukemia. WEE1 inhibitor AZD1775 and belinostat may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. 