Vorinostat, Azacitidine, and Gemtuzumab Ozogamicin for Older Patients With Relapsed or Refractory AML

Inclusion Criteria: * Prior morphological diagnosis of acute myeloid leukemia (AML) other then acute promyelocytic leukemia (APL) according to the 2001 WHO criteria; patients with biphenotypic AML are eligible * Need for first salvage chemotherapy for persistent or relapsing disease, defined by standard criteria, after at least one course of conventional chemotherapy * A bone marrow biopsy is not required but should be obtained if the aspirate is dilute, hypocellular, or not aspirable; outside marrow exams performed within the stipulated time period are acceptable if the slides are reviewed at the study institution * Flow cytometric analysis of the marrow aspirate per institutional practice guidelines * Duration of first complete remission (CR1) \< 12 months (or primary resistant disease) * Patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) if relapse occurs 6-12 months post-transplant * ECOG/WHO/Zubrod performance status of 0-3 within 14 days prior to registration * Off any active therapy for AML except hydroxyurea for at least 14 days prior to study registration, with resolution of all grade 3 and 4 non-hematological toxicities * Willingness to discontinue taking any medications known to cause a risk of Torsades de Pointes * Bilirubin =\< 1.5 x Institutional Upper Limit of Normal (IULN) unless elevation is due to hepatic infiltration by AML, Gilbert's syndrome, or hemolysis (within 7 days prior to registration) * SGOT (AST) and SGPT (ALT) =\< 1.5 x IULN unless elevation is due to hepatic infiltration by AML (within 7 days prior to registration) * Serum creatinine =\< 1.5 x IULN (within 7 days prior to registration) * No clinical or radiographical evidence of heart failure * white blood cell (WBC) \< 25,000/uL within 3 days prior to registration * Patients with symptoms/signs of hyperleukocytosis or WBC \> 100,000/uL can be treated with leukapheresis prior to enrollment * Collection of bone marrow and peripheral blood specimens for correlative studies prior to study treatment is highly recommended; peripheral blood only is acceptable if the peripheral blast count is \> 5,000/uL and \> 50% of total WBC * Must agree to use adequate contraception prior to and during the study * Can understand and sign a written informed consent document; a legally authorized representative can provide consent if the patient is unable Exclusion Criteria: * Remission or second or later relapse * Diagnosis of another malignancy, unless diagnosed at least 2 years earlier and disease-free for at least 6 months after completion of curative intent therapy except: * Treated non-melanoma skin cancer, in situ carcinoma, or cervical intraepithelial neoplasia, if definitive treatment has been completed * Organ-confined prostate cancer with no evidence of recurrent or progressive disease based on prostate-specific antigen (PSA) values if hormonal therapy has been initiated or a radical prostatectomy was performed * Refractory/relapsing blast crisis of chronic myeloid leukemia (CML) * Prior anti-AML treatment with GO, histone deacetylase (HDAC) inhibitor (including the use of valproic acid for control of seizure activity or other purposes), or demethylating agent * Known hypersensitivity to GO, vorinostat, azacitidine, or mannitol * Possible central nervous system (CNS) involvement with leukemia unless a lumbar puncture confirms no leukemic blasts in the cerebralspinal fluid (CSF) * HIV-positive patients with cluster of differentiation (CD)4 count is \< 200 cells/uL or if AIDS-related complications * Pregnancy; breastfeeding should be discontinued if the mother is treated with vorinostat, azacitidine, and GO * Uncontrolled systemic infection, despite appropriate antibiotics or other treatment) * Receipt of any other investigational agents