Pomalidomide After Combination Chemotherapy in Treating Patients With Newly Diagnosed Acute Myeloid Leukemia or High-Risk Myelodysplastic Syndrome

Inclusion Criteria: * Patients must have histologically or cytologically confirmed: * Pathologically confirmed intermediate or poor risk newly diagnosed AML (subtypes M0, 1, 2, 4-7), but excluding newly diagnosed core-binding factor (CBF) (t(8;21) or M4eo subtype (inv(16) or t(16;16) AMLs and acute promyelocytic leukemia (acute promyelocytic leukemia \[APL\], M3) * MDS with high risk features as defined by intermediate (INT)-2 or high International Prognostic Scoring System (IPSS) score with \> 10% blasts in the bone marrow * Chronic myelomonocytic leukemia-2 (CMML-2) defined as having \> 10% blasts (including promonocytes) in the bone marrow or 5-19% blasts (including promonocytes) in the peripheral blood * Patients who have received hydroxyurea alone or have received non-cytotoxic therapies previously for treatment of MDS or myeloproliferative neoplasm (MPN) (e.g. azacitidine, decitabine, histone deacetylase inhibitors, tyrosine kinase inhibitors, hematopoietic growth factors, interferon, lenalidomide, thalidomide) will be eligible for this trial as long as immunomodulatory drugs (e.g. lenalidomide, thalidomide) have not been used in the past 3 months * Patients must be off all non-cytotoxic chemotherapies or biologic agents (e.g. azacitidine, decitabine, histone deacetylase inhibitors, tyrosine kinase inhibitors, hematopoietic growth factors, interferon, but excluding hydroxyurea and cyclophosphamide) for at least 2 weeks prior to starting induction chemotherapy * Patients must be off radiation therapy or chemotherapy 4 weeks (6 weeks for nitrosoureas or mitomycin C) of starting induction chemotherapy * All adverse events (excluding alopecia, acne, rash) due to agents administered more than 2 weeks earlier should recover to =\< grade 1; patients with hematologic malignancies are expected to have hematologic abnormalities at study entry; these abnormalities which are thought to be primarily related to the underlying leukemia, are not considered to be toxicities (adverse events \[AE\]) and do not need to resolve to =\< grade 1 * Patients with therapy-related AML or MDS should have not received prior cumulative anthracycline (daunorubicin equivalent) lifetime dose \> 450 mg/m\^2 * Cytoreduction allowed: * Hydroxyurea, corticosteroids, leukapheresis can be used prior to start of induction chemotherapy * Cyclophosphamide up to dose 50-60 mg/kg is allowed for cytoreduction, but must be given at least 7+/- 2 days before start of induction chemotherapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 50%) * Total bilirubin \< 2.0 mg/dL unless due to Gilbert's disease, hemolysis or leukemia * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 x institutional upper limit of normal unless due to leukemic infiltration * Creatinine =\< 2.0 mg/dL * Left ventricular ejection fraction \>= 45% * Female who is able to become pregnant must have a negative pregnancy test with a sensitivity of at least 25 mIU/mL within 10-14 days prior to and again within 24 hours of starting pomalidomide; female who is able to become pregnant must either commit to continued abstinence from heterosexual intercourse or begin two acceptable methods of birth control, one highly effective and one additional effective method at the same time; female who is able to become pregnant must agree to ongoing pregnancy testing; men must agree to use a latex condom during sexual contact with female who is able to become pregnant even if they had vasectomy for the duration of study participation, and 28 days after completion of pomalidomide administration; all patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure while taking pomalidomide; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately * A female who is able to become pregnant is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Ability to understand and the willingness to sign a written informed consent document; consent will be obtained by day 14 of AcDVP-16 induction regimen * Known human immunodeficiency virus (HIV) infected patients (HIV testing will not be performed as a part of screening) on combination antiretroviral therapy are eligible for inclusion; the use of zidovudine is not allowed Exclusion Criteria: * Patients who are receiving any other investigational agents or who have received pomalidomide in the past * Patients with known active central nervous system leukemia should be excluded from this clinical trial; patient receiving intrathecal chemotherapy prophylaxis should not receive pomalidomide for \>= 3 days after administration * History of allergic reactions attributed to compounds of similar chemical or biologic composition to pomalidomide (e.g. lenalidomide, thalidomide) or other agents used in study * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide, lenalidomide or similar drugs in the past * Uncontrolled intercurrent illness including, but not limited to, active and uncontrolled infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, mental deficits, psychiatric illness or history or social situations that would limit compliance with study requirements; patients with infection under active treatment and controlled with antibiotics are eligible * Any other medical condition that in opinion of investigator would place patient at increased risk for toxicity during pomalidomide treatment (i.e. history of recurrent or serious thromboembolic events) * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with pomalidomide * Known positive patients for infectious hepatitis, type A, B, C * Active graft-versus-host disease (GVHD) following allogeneic stem cell transplant for non-AML condition (ex. MDS, MPN, lymphoid malignancy, aplastic anemia) requiring ongoing use of immunosuppressants