Ruxolitinib Phosphate and Azacytidine in Treating Patients With Myelofibrosis or Myelodysplastic Syndrome/Myeloproliferative Neoplasm

Inclusion Criteria: * Patients with a diagnosis of primary myelofibrosis (PM), post polycythemia vera myelofibrosis (PPV MF), or post essential thrombocythemia myelofibrosis (PET MF) requiring therapy, including those previously treated and relapsed or refractory, or if newly diagnosed, with intermediate or high risk according to International Working Group (IWG-MRT) criteria * Patients with a diagnosis of myelodysplastic syndrome/myeloproliferative neoplasm, unclassifiable (MDS/MPN-U) that require therapy * Understanding and voluntarily signing an Institutional Review Board (IRB)-approved informed consent form * Eastern Cooperative Oncology Group (ECOG) performance status 0 to 2 * Direct bilirubin of =\< 2 mg/dL * Serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x upper limit of normal (ULN) or 5 x ULN if related to MF or MDS/MPN associated liver infiltration * If total bilirubin is =\< 2, fractionation is not required for eligibility determination * Creatinine =\< 2.5 mg/dL * Platelets \>= 50 x 10\^9/L * Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L Exclusion Criteria: * For the MF and MDS/MPN-U arms (arms 1 \& 2), use of any other standard drug (except hydroxyurea, anagrelide, growth factors, Revlimid, clofarabine, etc) or experimental drug or therapy within 14 days of starting study therapy * Patients previously treated with RUX or AZA (only applicable for the MF and MDS/MPN arms) * Any serious psychological condition or psychiatric illness that would prevent t…