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 the subject from signing the informed consent document, in the investigator opinion * Pregnant or lactating females * Subjects of childbearing potential who are unwilling to take appropriate precautions (from screening through follow-up) to avoid becoming pregnant or fathering a child; females of non-childbearing potential are defined as women who a) are 55 years of age with history of amenorrhea for 1 year OR b) are surgically sterile for at least 3 months; for females of childbearing potential, or for males, pregnancy must be avoided by taking appropriate precautions; these precautions and the methods of contraception should be communicated to the subjects and their understanding confirmed * Any condition which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * Known positive for human immunodeficiency virus (HIV) or with known active infectious hepatitis, type A, B or C * Patients with active malignancy of other type than required for this study, are not eligible with the exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast; patients with malignancies with indolent behavior such as prostate cancer treated with radiation or surgery can be enrolled in the study as long as they have a reasonable expectation to have been cured with the treatment modality received