Vorinostat, Tacrolimus, and Methotrexate in Preventing GVHD After Stem Cell Transplant in Patients With Hematological Malignancies

Inclusion Criteria: * A prospective patient for allogeneic HSCT for hematologic conditions, both malignant and non-malignant; donor can be unrelated marrow or peripheral blood cells; a patient with history of central nervous system (CNS) involvement is eligible if CNS disease is in remission at time of study consideration * The donor and recipient must have a human leukocyte antigen (HLA)-8/8 allelic match at the HLA-A, -B, -C, and -DRB1; high-resolution typing is required for all alleles * Diagnoses to be included: * Acute myelogenous leukemia at the following stages: * First remission * Second or subsequent remission * Complete remission is defined as the absence of blasts in the peripheral circulation at the time of enrollment and \< 5% blasts in the bone marrow * Chronic myelogenous leukemia at the following stages: * First or subsequent chronic phase: * Patient refused tyrosine kinase therapy or is otherwise not suited for it * Stable, not hematologic remission: blasts present in marrow and/or peripheral blood, but disease does not qualify as accelerated or blast phase * Hematologic remission: no blast cells or precursor cells in the blood or marrow * Partial cytogenetic remission: Philadelphia chromosome positive (Ph+) metaphases \> 0% but \< 35% * Complete cytogenetic remission: absence of Ph+ metaphases * Accelerated phase - any one of the following symptoms: * White blood cells (WBC) difficult to control (\> 50 x 10\^9/L despite therapy) * Rapid doubling of WBC (\< 5 days) * 10% blasts in blood or marrow * 20% blasts and/or promyelocytes in blood or marrow * 20% basophils and/or eosinophils in blood * Anemia or thrombocytopenia unresponsive to standard treatment * Persistent thrombocytosis (\> 1000 x 10\^9/L) * Cytogenetic abnormalities in addition to Ph+ * Increasing splenomegaly * Marrow fibrosis * Myelodysplastic syndromes at any of the following stages: * Refractory anemia * Refractory anemia with ringed sideroblasts * Refractory cytopenia with multilineage dysplasia * Refractory cytopenia with multilineage dysplasia and ringed sideroblasts * Refractory anemia with excess blasts-1 (5-10% blasts) * Refractory anemia with excess blasts-2 (10-20% blasts) * Myelodysplastic syndrome, unclassified * Myelodysplastic syndrome (MDS) associated with isolated del (5q) * Chronic myelomonocytic leukemia * Primary Myelofibrosis * Intermediate-2 risk or high risk disease * Patients should have extinguished standard of care options prior to being considered for this trial * Chronic lymphocytic leukemia * Complete remission: the disease is completely absent and no relapse occurred prior to the preparative regimen; requires all of the following: * Nodular partial remission: complete response with persistent lymphoid nodules in bone marrow * Partial remission: reduction of more than 50% in the disease burden regardless of the number of lines of therapy received * Mature B cell malignancies * Patients should have extinguished standard of care options prior to being considered eligible for this trial * First complete remission (CR1) confirmed: complete disappearance of all known disease; the term "confirmed" is defined as a laboratory and/or pathological or radiographic determination. * CR1 unconfirmed (CRU1): complete disappearance of all known disease with the exception of persistent scan abnormalities of unknown significance; the term "unconfirmed" is defined as scan abnormalities of unknown significance that are not biopsied or otherwise evaluated * Second or subsequent complete remission (CR2+) confirmed: the recipient relapsed, then achieved complete absence of disease without radiographic evidence of disease * CR2+ unconfirmed: the recipient has achieved a second or subsequent complete response but has persistent radiographic abnormalities of unknown significance. * Partial remission: reductions of \>= 50% in greatest diameter of all sites of known disease and no new sites * Karnofsky \>= 70% * Life expectancy of greater than 6 months * Total bilirubin =\< 2.5 mg% (unless from Gilbert's disease or disease-related) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 3.0 X institutional upper limit of normal * Estimated or actual glomerular filtration rate (GFR) \> 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal; GFR should be corrected for body surface area (BSA) * Diffusing capacity of the lung for carbon monoxide (DLCO) \> 50%; DLCO should be corrected for hemoglobin * Forced expiratory volume in 1 second (FEV1) \> 50% * Forced vital capacity (FVC) \> 50% * Ejection fraction \>= 50% * The effects of vorinostat on the developing human fetus are unknown; for this reason and because histone deacetylase inhibitor agents as well as other therapeutic agents used in this trial (e.g., tacrolimus and methotrexate) are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of vorinostat administration * Ability to understand and the willingness to sign a written informed consent document * Patients must be able to swallow capsules/tablets Exclusion Criteria: * Patients who are not a candidate for an unrelated donor allogeneic HSCT based on the current institutional bone marrow transplant (BMT) program clinical practice guidelines; organ function criteria will be utilized per the current institutional BMT program clinical practice guidelines; there will be no restriction to study entry based on hematological parameters * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat * Patients undergoing a total body irradiation (TBI)-based conditioning regimen (TBI 1200 centigray \[cGy\]) * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements; patients still under therapy for presumed or proven infection are eligible provided there is clear evidence (radiographic findings and/or culture results) that the infection is well-controlled; patients under treatment for infection will be enrolled only after clearance from the Principal Investigator (PI) * Pregnant women are excluded from this study because vorinostat is a histone deacetylase inhibitor agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with vorinostat, breastfeeding should be discontinued if the mother is treated with vorinostat * Patients with evidence of human immunodeficiency virus (HIV) seropositivity and/or positive polymerase chain reaction (PCR) assay, human T-lymphotropic virus (HTLV)1/HTLV2 seropositivity; the safety of allogeneic HSCT is not yet well-established for this population * Patients with evidence of hepatitis B or hepatitis C PCR positivity; hepatitis reactivation following myelosuppressive therapy can lead to fatal complications * Patients with a history of prolonged corrected QT interval (QTc) syndrome * Patients asking or who have had prior treatment with a drug like vorinostat (i.e., valproic acid) within the last 30 days