OX40, Venetoclax, Avelumab, Glasdegib, Gemtuzumab Ozogamicin, and Azacitidine in Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * ARMS A-G: RR AML: Patients with AML who are refractory or relapsed (any salvage) with no available therapies or not candidates for available therapies. For patients with prior MDS or chronic myelomonocytic leukemia (CMML) or myeloproliferative neoplasm (MPN) who transformed to AML, therapy received for MDS, CMML, or MPN is NOT considered as prior therapy for AML with the exception of MDS or CMML treated with hypomethylating agents (HMAs). Patients with MDS or CMML treated with HMA therapies who progress to AML, and have no available therapies or are not candidates for available therapies, will be eligible at the time of progression to AML. * Prior therapy with hydroxyurea, chemotherapy, biological or targeted therapy (e.g. FLT3 inhibitors, other kinase inhibitors), or hematopoietic growth factors is permitted. * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2. * Total bilirubin =\< 2.0 times upper limit of normal (x ULN). * Aspartate aminotransferase or alanine aminotransferase =\< 2.5 x ULN (aspartate aminotransferase or alanine aminotransferase =\< 5.0 x ULN if deemed related to leukemia by the treating physician). * Adequate renal function defined by an estimated creatinine clearance \>= 40 mL/min according to the Cockcroft-Gault formula (or local institutional standard method). * Patients must provide written informed consent. * In the absence of rapidly progressive disease, the interval from prior treatment to the time of initiation of protocol therapy will be at least 14 days for prior anti-leukemic therapy, with the exception of hydroxyurea as noted below, OR at least 5 half-lives for cytotoxic/noncytotoxic agents, whichever is shorter. The half-life for the therapy in question will be based on published pharmacokinetic literature (abstracts, manuscripts, investigator brochure's, or drug-administration manuals) and will be documented in the protocol eligibility document. The toxicity from prior therapy should have resolved to grade =\< 1, however alopecia and sensory neuropathy grade =\< 2 not constituting a safety risk based on investigators judgement is acceptable. Since the effect of most IO-agents, HMA-therapies, SMO-inhibitors, venetoclax may be delayed, use of hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and will not require a washout. * Concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted. Patients with a known history of CNS disease or leukemic brain metastasis must have been treated locally, have at least 3 consecutive lumbar punctures (LPs) with no evidence of CNS leukemia, and must be clinically stable for at least 4 weeks prior to enrollment and have no ongoing neurological symptoms that in the opinion of the treating physician are related to the CNS disease (sequelae that are a consequence of the treatment of the CNS disease are acceptable). * Females must be surgically or biologically sterile or postmenopausal (amenorrheic for at least 12 months) or if of childbearing potential, must have a negative serum or urine pregnancy test within 72 hours before the start of the treatment. * Women of childbearing potential must agree to use an adequate method of contraception during the study and until 3 months after the last treatment. Males must be surgically or biologically sterile or agree to use an adequate method of contraception during the study until 3 months after the last treatment. Adequate methods of contraception include: * Total abstinence when this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception. * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy) or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment. * Male sterilization (at least 6 months prior to screening). For female patients on the study, the vasectomized male partner should be the sole partner for that patient. * Combination of any of the two following: * Use of oral, injected or implanted hormonal methods of contraception or other forms of hormonal contraception that have comparable efficacy (failure rate \< 1%), for example hormone vaginal ring or transdermal hormone contraception. * Placement of an intrauterine device (IUD) or intrauterine system (IUS). * Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/ vaginal suppository in case of use of oral contraception, women should have been stable on the same pill before taking study treatment. * Note: Oral contraceptives are allowed but should be used in conjunction with a barrier method of contraception due to unknown effect of drug-drug interaction. Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago. In the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential. Exclusion Criteria: * Patients with a known allergy or hypersensitivity to the protocol therapies or any of their components to be used in the arm the patient is to be enrolled on. Known severe hypersensitivity reactions to monoclonal antibodies (grade \>= 3 National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 4.03), any history of anaphylaxis, or uncontrolled asthma (that is, 3 or more features of partially controlled asthma). * Patients with a known history of severe interstitial lung disease or severe pneumonitis or active pneumonitis/pneumonia or pulmonary pathology that is not well controlled in the opinion of the treating physician and/or principal investigator (PI). * Clinically significant (i.e., active) cardiovascular disease: acute cerebral vascular accident/stroke (\< 6 months prior to enrollment) excluding transient ischemic attack (TIA), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (\>= New York Heart Association classification class II), or serious cardiac arrhythmia requiring medication. * Ejection fraction \< 50% on screening echocardiography (ECHO) or multigated acquisition scan (MUGA). * Persisting toxicity related to prior therapy of grade \> 1 NCI-CTCAE v 4.03; however, alopecia and sensory neuropathy grade =\< 2 is acceptable. * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent: \* Subjects with diabetes type I, vitiligo, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible * Current use of immunosuppressive medication, EXCEPT for the following: * Intranasal, inhaled, topical steroids, or local steroid injection (e.g., intra-articular injection); * Systemic corticosteroids at physiologic doses =\< 10 mg/day of prednisone or equivalent; * Steroids as premedication for hypersensitivity reactions (e.g., computed tomography \[CT\] scan premedication). * Prior organ transplantation including allogenic stem-cell transplantation within 3 months prior to planned enrollment. * Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia. * Active and uncontrolled disease (active infection requiring systemic therapy, fever likely secondary to infection within prior 48 hours, uncontrolled hypertension despite adequate medical therapy as judged by the treating physician. * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome. * Known history of hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive HBV surface antigen or HCV RNA if anti-HCV antibody screening test positive. * Vaccination within 4 weeks of the first dose of avelumab and while on trials is prohibited except for administration of inactivated vaccines. * Other severe acute or chronic medical conditions that is active and not well controlled including colitis, inflammatory bowel disease, or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. * Patients unwilling or unable to comply with the protocol. * Pregnant or breastfeeding. * Known alcohol or drug abuse within the last 1 year. * Acute promyelocytic leukemia (APL). * Cardiac exclusions specific to glasdegib and OX40 containing arms: Any one of the following ongoing or in the previous 6 months: congenital long QT syndrome, torsades de pointes or any clinically significant ventricular fibrillation, sustained ventricular tachyarrhythmia requiring medical intervention, right bundle branch block + left anterior hemiblock (i.e. bifascicular block): isolated RBBB without a bifascicular block will not be an exclusion criterion; complete left bundle branch block, unstable angina or myocardial infarction, coronary/peripheral artery bypass graft, cerebrovascular accident (CVA), transient ischemic attack or symptomatic pulmonary emboli, as well as bradycardia defined as \< 50 bpms on screening or day 1 electrocardiography (EKG). Known history of second or third degree heart block (may be eligible if the patient currently has a pacemaker). Active cardiac dysrhythmias of NCI CTCAE grade \>= 2 (eg, atrial fibrillation) or corrected QT interval by Fridericia's correction formula (QTcF) interval \> 470 msec within 4 weeks prior to starting the study drug