Azacitidine, Venetoclax, and Pevonedistat in Treating Patients With Newly Diagnosed Acute Myeloid Leukemia

Inclusion Criteria: * AML COHORT ONLY: Patients must have a new diagnosis (i.e., no prior therapy for AML) of AML per World Health Organization (WHO) 2016 criteria and any one of the following (i.e. therapy-related AML or AML with myelodysplastic-related changes per WHO): * A history of MDS * A history of a myeloproliferative neoplasm (MPN) including polycythemia vera (PV), essential thrombocythemia (ET), myelofibrosis (MF, whether primary \[pre-fibrotic or overt\] or post-polycythemia vera \[PV\]/essential \[E\]), chronic neutrophilic leukemia (CNL), chronic eosinophilic leukemia (CEL), MPN-unclassifiable (MPN-U) or myeloid neoplasm with a rearrangement of PDGFRA, PDGFRB or FGFR1 * A history of MDS/MPN such as chronic myelomonocytic leukemia (CMML), MDS/MPN-unclassifiable (MDS/MPN-U), MDS/MPN with ringed sideroblasts and thrombocytosis (MDS/MPN-RS-T) or atypical chronic myeloid leukemia (aCML), BCR-ABL negative * An MDS-related cytogenetic abnormality other than del9q * The presence of dysplasia in \>= 50% cells in \>= 2 myeloid lineages, unless accompanied by mutant NPM1 or biallelic CEBPA mutations * Exposure to prior chemotherapy or radiation therapy for another malignancy * NEWLY DIAGNOSED MDS/CMML COHORT ONLY: Diagnosis of MDS or CMML with intermediate-2 or high-risk disease by the International Prognostic Scoring System (IPSS) * MDS/CMML POST-HMA FAILURE COHORT ONLY: Diagnosis of MDS or CMML with intermediate-1, intermediate-2, or high-risk disease by the IPSS who have no responded, progressed, or relapsed after treatment with at least 4 cycles of azacitidine and/or decitabine * Eastern Cooperative Oncology Group (ECOG) performance status from 0-2 * Total bilirubin =\< 1.5 x upper limit of normal (ULN) except in patients with Gilbert's syndrome or if elevation is attributed to underlying leukemia. Patients with Gilbert's syndrome or with elevated bilirubin attributed to underlying leukemia may enroll if direct bilirubin =\< 1.5 x ULN of the direct bilirubin (repeat if more than 3 days before the first dose) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN (repeat if more than 3 days before the first dose) * Creatinine clearance \>= 30 mL/min (repeat if more than 3 days before the first dose) * White blood cell (WBC) count \< 50,000/uL. Note: Hydroxyurea may be used to control leukocytosis for the first 28 days of study treatment (i.e., cycle 1). Use of hydroxyurea beyond this point may be permitted as clinically indicated, on a case-by-case basis and after discussion with the principal investigator (PI). (repeat if more than 3 days before the first dose) * Female patients who: * Are postmenopausal for at least 1 year before the screening visit, OR * Are surgically sterile, OR * If they are of childbearing potential: * Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception) * Male patients, even if surgically sterilized (i.e., status postvasectomy), who: * Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), or * Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods for the female partner\] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception.) * Voluntary written consent must be given before performance of any study related procedure Exclusion Criteria: * Treatment with any investigational anti-neoplastic drugs within 2 weeks before the first dose of any study drug (cycle 1 day 1 \[C1D1\]) * AML COHORT ONLY: Patients who are suitable for and agreeable to receive intensive induction chemotherapy * NEWLY DIAGNOSED MDS/CMML COHORT ONLY: Prior treatment with hypomethylating agents * MDS/CMML POST-HMA FAILURE COHORT ONLY: Prior treatment with venetoclax or pevonedistat * Patients whose only site of disease is extramedullary * Acute promyelocytic leukemia as diagnosed by morphologic examination of bone marrow, by fluorescent in situ hybridization or cytogenetics of peripheral blood or bone marrow, or by other accepted analysis * Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of study procedures * Active uncontrolled infection or severe infectious disease, such as severe pneumonia, meningitis, or septicemia * Major surgery within 14 days before the first dose of any study drug * Patients with a prior or concurrent malignancy whose natural history or treatment is not anticipated to interfere with the safety or efficacy assessment of the investigational regimen may be included only after discussion with the PI * Life-threatening illness unrelated to cancer, leading to expected life expectancy (unrelated to leukemia) \< 1 year * Patients with severe, uncontrolled coagulopathy or bleeding disorder not related to leukemia * Known human immunodeficiency virus (HIV) positive patients who meet the following criteria will be considered eligible: * CD4 count \> 350 cells/mm\^3 * Undetectable viral load * Maintained on modern therapeutic regimens utilizing non-CYP-interactive agents * No history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections * Known hepatitis B surface antigen seropositive or known or suspected active hepatitis C infection * Note: Patients who have isolated positive hepatitis B core antibody (i.e., in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load. Patients who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load * Known hepatic cirrhosis or severe pre-existing hepatic impairment * Known cardiopulmonary disease defined as: * Unstable angina within 6 months * Congestive heart failure (New York Heart Association \[NYHA\] class III or IV) * Myocardial infarction (MI) within 6 months prior to first dose (patients who had ischemic heart disease such as an acute coronary syndrome \[ACS\], MI, and/or revascularization greater than 6 months before screening and who are without cardiac symptoms may enroll) * Symptomatic cardiomyopathy * Clinically significant arrhythmia * History of polymorphic ventricular fibrillation or torsade de pointes * Persistent atrial fibrillation (a fib) requiring cardioversion in the 4 weeks before screening * Grade 3 a fib defined as symptomatic and incompletely controlled medically , or controlled with device (e.g. pacemaker), or ablation in the past 6 months * Moderate to severe aortic and/or mitral stenosis or other valvulopathy (ongoing) * Symptomatic pulmonary hypertension requiring pharmacologic therapy * Uncontrolled high blood pressure (i.e., systolic blood pressure \> 180 mm Hg, diastolic blood pressure \> 100 mm Hg documented on two consecutive blood pressure evaluations) * Prolonged rate corrected QT (QTc) interval \>= 500 msec, calculated according to institutional guidelines * Left ventricular ejection fraction (LVEF) \< 50% as assessed by echocardiogram or radionuclide angiography * Known severe chronic obstructive pulmonary disease, interstitial lung disease, and pulmonary fibrosis * Known central nervous system (CNS) involvement * Treatment with strong CYP3A4 inducers within 14 days (or 3 half-lives, whichever is shorter) before the first dose of the study drug. Strong CYP3A4 inducers are not permitted during this study * Systemic antineoplastic therapy or radiotherapy for other malignant conditions within 14 days (or 3 half-lives, whichever is shorter) before the first dose of any study drug, except for hydroxyurea or up to 2 total grams of intravenous cytarabine for cytoreduction. Prior hypomethylating agent (HMA) therapy is allowed, unless given for AML * Female patients who are either lactating and/or breastfeeding or have a positive serum pregnancy test during the screening period * Female patients who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s) * Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s) * Known hypersensitivity to azacitidine, mannitol or pevonedistat, any of their components, or compounds of similar chemical composition