Azacitidine and Oxaliplatin In Treating Patients With Advanced Cancers Relapsed or Refractory to Any Platinum Therapy

Inclusion Criteria: * Patients must have histologically confirmed malignancy (solid tumor or lymphoma) that is metastatic or unresectable and for which standard curative or palliative measures are not expected to increase survival by at least 3 months * Patients must have an advanced cancer relapsed or refractory to any platinum compound; platinum-refractory disease is defined as disease that does not respond to a platinum compound-containing regimen or that recurs after treatment with a platinum compound-containing regimen * Patients must have had \>= 1 prior chemotherapy regimen; there is no maximum allowable number of prior regimens, provided all other eligibility criteria are met * Patients must be \>= 6 weeks beyond treatment with a nitrosourea or mitomycin-C, \>= 4 weeks beyond other chemotherapy or radiotherapy, and must have recovered to =\< grade 1 toxicity for any treatment-limiting toxicity of prior therapy; (exception: patients may have received palliative low-dose radiotherapy to the limbs 1-4 weeks before this therapy, provided pelvis, ribs, sternum, scapulae, vertebrae, or skull were not included in the radiotherapy field) * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 4,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin =\< 1.0 mg/dL * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 X institutional upper limit of normal * Creatinine (serum) =\< 2.0 mg/dL * International normalized ratio (INR) of less than or equal to 1.75 per institutional guideline * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Patients must have the ability to understand and the willingness to sign a written informed consent document, including consent for the required tumor biopsy (in the expansion phase), blood, and pharmacokinetics studies * Tumor should be accessible for repeat biopsy if in the expansion phase; biopsies will be performed in the expansion phase; the expansion cohort will be between 10 and 20 patients * Patients must have expected survival of at least 3 months Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered to =\< grade 1 treatment-limiting toxicity levels for adverse events due to agents administered more than 4 weeks earlier; (exception: patients may have received palliative low dose radiotherapy to the limbs 1-4 weeks before this therapy, provided pelvis, ribs, sternum, scapulae, vertebrae, or skull were not included in the radiotherapy field) * Patients may not be receiving any other concurrent investigational agents * Patients must not have a history of allergic reactions attributed to 5-azacytidine, oxaliplatin, or compounds with a similar composition * Patients must not have oxaliplatin intolerance * Patients must not have uncontrolled intercurrent illness, including but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, potentially life-threatening cardiac arrhythmia, and psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with 5-azacytidine * Patients known to be human immunodeficiency virus (HIV)-positive and receiving anti-retroviral therapy must have both a minimum of 350 CD4+ cells/mm\^3 and no history of acquired immunodeficiency syndrome (AIDS) defining conditions except for lymphoma * Patients who have had surgery within 2 weeks prior to entering the study are not eligible * Patients who have been removed from prior platinum-containing therapy due to platinum-compound cumulative toxicity