Neoadjuvant Chemotherapy Followed by Radiation Therapy and Gemcitabine/Sorafenib/Vorinostat in Pancreatic Cancer

Inclusion Criteria: * Adenocarcinoma of the pancreas * Prior therapy with ≥ 1 prior systemic therapy over a period of at least 2 months (eg, at least two 4-week cycles of a regimen such as gemcitabine and nab-paclitaxel; or at least four 2-week cycles of a regimen such as FOLFOX, FOLFIRINOX, or FOLFIRI) -Candidate for additional therapy consisting of radiation with gemcitabine- radiosensitization. * Able to initiate study treatment no later than 9 weeks from last dose of any antineoplastic component of prior therapy regimen. * Recovery from ≥ grade 2 toxicities of prior therapy regimen to grade 1 or baseline, with the exception of anemia and lymphopenia and chronic residual toxicities that in the opinion of the investigator are not clinically relevant given the known safety/toxicity profiles of gemicitabine, sorafenib, and vorinostat (eg, alopecia, changes in pigmentation, stable endocrinopathies). Patients with ≤ grade 2 peripheral sensory or motor neuropathy are eligible.. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \<= 3 x upper limit of normal (ULN) for the laboratory * Total bilirubin \<= 1.5 x ULN for the laboratory at the time of enrollment, all forms of biliary stents allowed * Creatinine clearance \>= 45 mL/min as calculated by the standard Cockcroft-Gault equation using age, actual weight, creatinine and gender * International normalized ratio (INR) \<= 1.5 * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 (may not be transfused to meet this level for enrollment) * Measurable or evaluable disease by Response Evaluation Criteria in Solid Tumors (RECIST) (version \[v\]1.1 * Ability to understand and the willingness to sign a written informed consent document * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment * Women of childbearing potential and men must agree to use a medically accepted form of birth control during the treatment and for 2 months following completion of study treatment Exclusion Criteria: * Prior radiotherapy for pancreatic cancer * Prior surgical resection of pancreatic cancer * Evidence of metastatic disease * Any investigational agent within 4 weeks of study treatment initiation * Diagnosis or treatment for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, any in situ malignancy, or low-risk prostate cancer after curative therapy * Intolerance of protocol agents as follows: * Known or presumed intolerance of gemcitabine, vorinostat or sorafenib * Experienced any of the following toxicities with prior gemcitabine adminstration (if given): capillary leak syndrome, posterior reversible encephalopathy, hemolytic uremic syndrome, thrombotic thrombocytopenic purpura, unexplained dyspnea or other evidence of severe pulmonary toxicity, or severe hepatic toxicity * Unable to swallow medication * Suspected malabsorption or obstruction; note: use of pancreatic enzyme supplements is allowed to control malabsorption * Contraindication to antiangiogenic agents, including: * Bronchopulmonary hemorrhage/bleeding event \>= grade 2 (Common Terminology Criteria for Adverse Events \[CTCAE\] v4.0) within 12 weeks prior to of treatment * Any other hemorrhage/bleeding event \>= grade 3 (CTCAE v4.0) within 12 weeks prior to initiation of treatment * Serious non-healing wound, ulcer, or bone fracture * Arterial thrombotic or embolic events such as a myocardial infarction or cerebrovascular accident (including transient ischemic attacks) within the 6 months prior to initiation of treatment. Incidental clinically insignificant embolic phenomena that do not require anti-coagulants are not excluded. Also,tumor-associated thrombus of locally-involved vessels does not count as an exclusion criterion. * Clinically significant cardiac disease, including major cardiac dysfunction, such as uncontrolled angina, clinical congestive heart failure with New York Heart Association (NYHA) class III or IV, ventricular arrhythmias requiring anti-arrhythmic therapy, recent (within 6 months) myocardial infarction or unstable coronary artery disease * Concomitant use of other histone deacetylase (HDAC) inhibitors * Planned ongoing administration of STRONG cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inducers. Examples of clinical inducers and classifications of strong, moderate, and weak interactions are available through the FDA website (Table 3-3 of website): http://www.fda.gov/Drugs/DevelopmentApprovalProcess/DevelopmentResources/DrugInteractionsLabeling/ucm093664.htm * Persistent heart rate (HR) \< 50 or \> 120 beats per minute (bpm). * QT(c) ≥ 481 ms (\>= grade 2) on electrocardiogram (ECG) prior to initiation of treatment * If baseline QTc on screening ECG meets exclusion criteria: * Check potassium and magnesium serum levels * Correct any identified hypokalemia and/or hypomagnesemia and repeat ECG to confirm exclusion of patient due to QTc * For patients with HR \>60 of \>100 beats per minute (bpm), no manual read of QTc is required * For patients with baseline HR \< 60 or \> 100 bpm, manual read of QT by cardiologist is required, with Fridericia correction applied to determine QTc * Planned ongoing treatment with other drugs thought to potentially adversely interact with study drugs; if such medications have been used, patients must be off of these agents for \>= 2 weeks prior to initiation of treatment: * Anticoagulants at therapeutic doses * Immunosuppressants such as tacrolimus, leflunomide or tofacitinib, roflumilast, pimecrolimus * Serious uncontrolled infection \> grade 2 (CTCAE v4.0) * Medical, psychological, or social conditions that, in the opinion of the investigator, may increase the patient's risk or interfere with the patient's participation in the study or hinder evaluation of the study results