Sorafenib, Valproic Acid, and Sildenafil in Treating Patients With Recurrent High-Grade Glioma

Inclusion Criteria: * Pathologically confirmed high-grade glioma (World Health Organization (WHO) grade 3 or 4), with documented computed tomography (CT) or magnetic resonance imaging (MRI) progression or recurrence. Biopsy is also an acceptable method of confirming progression or recurrence. If initial tumor was grade 2 glioma, histological confirmation of high-grade recurrence is required * After first interim analysis, if the study proceeds to enrollment of selected patients (only those who have platelet-derived growth factor receptor (PDGFRa)-positive tumors), patients will be pre-registered for PDGFRa analysis and registered to the combination treatment schema only if PDGFRa-positive an all other enrollment criteria are met. * Measurable or evaluable disease by response assessment in neuro-oncology (RANO) (MRI) or MacDonald (CT) criteria * Fixed or decreasing dose of corticosteroids (or no corticosteroids) for at least 1 week prior to cycle 1 day 1. * At least 12 weeks since the completion of radiation therapy to a total of \>=50 Gray (Gy). * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * White blood cell (WBC) \>= 3,000/mm\^3 * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelets \>= 100,000/mm\^3 * Hemoglobin (Hgb) \>= 8.5 g/dL * Aspartate aminotransferase (AST), alanine aminotransferase (ALT) =\< 3 x upper limit of normal (ULN) for the laboratory * Total bilirubin =\< 1.5 x ULN for the laboratory (total bilirubin criteria may be waived if a patient has documented Gilbert's disease) * Creatinine clearance (CrCL) \>= 30 mL/min as calculated by standard Cockcroft-Gault equation * 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 for the duration of study participation and for 2 months following completion of study treatment. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Investigational agent within 4 weeks of first dose of study treatment * Prior bevacizumab or tyrosine-kinase inhibitor * History of allergic reactions or intolerance to any of the required agents on the study * Any condition that would prohibit patient from initiating valproic acid. Current or prior valproic acid treatment is allowed (do not need to be ≥ LLN for laboratory for enrollment). * Seizure disorder necessitating the use of enzyme-inducing antiepileptic drugs (EIAEDs). Efforts may be made by the treating physician to change the antiepileptic drug from another agent to valproic acid or non-EIAED prior to excluding the patient from study * Contraindication to antiangiogenic agents, including: * Bronchopulmonary hemorrhage/bleeding event \>= grade 2 (NCI Common Terminology Criteria for Adverse Events \[CTCAE\] version 4.0) within 4 weeks or less prior to first dose of study drug * Any other hemorrhage/bleeding event \>= grade 3 (NCI CTCAE v4.0) within 4 weeks or less prior to first dose of study treatment * Radiological evidence of any intracranial hemorrhage within the 4 weeks or less less prior to first dose of study treatment * History of significant intratumoral, intracerebral, or subarachnoid hemorrhage * Serious non-healing wound, ulcer, or bone fracture * Documented bowel perforation within 6 months of the start of study treatment. * Major surgery within 2 weeks of the start of study treatment, or ongoing complications from surgeries performed previously * 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 higher, ventricular arrhythmias requiring antiarrhythmic therapy, recent (within 6 months) myocardial infarction or unstable coronary artery disease. * Systolic blood pressure (BP) \> 160 mm Hg or diastolic pressure \> 100 mm Hg despite optimal medical management * History of priapism * Known history of retinitis pigmentosa * Known mitochondrial disorder caused by mutations in mitochondrial DNA polymerase γ. * Arterial thromboembolic or embolic events such as myocardial infarction, cerebrovascular accident, including transient ischemic attacks 6 months prior to first study treatment * Serious uncontrolled infection \> grade 2 (CTCAE v 4) * Known human immunodeficiency virus (HIV) positivity * Unable to swallow medication or suspected malabsorption * Patients on chronic nitrate therapy or alpha-blockers \* Exclude persons who require ongoing administration of STRONG CYP3A4 inhibitors and/or STRONG CYP3A4 inducers and/or STRONG CYP2C9 inhibitors. * Women who are pregnant or nursing * Persistent heart rate (HR) \<50 or \>120 beats per minute (bpm) * Corrected QT (QTc) \> 480 ms (grade 2 or greater) on screening electrocardiogram (ECG) \* If baseline QTc on screening ECG meets exclusion criteria on screening assessment: * Check potassium and magnesium levels * Correct any identified hypokalemia and/or hypomagnesemia and repeat ECG to confirm exclusion of patient due to QTc * For patients with a heart rate (HR) 60-100 bpm, no manual read of QT is required * For patients with baseline HR \< 60 or \> 100 bpm, manual read of QT by cardiologist is required using Fridericia correction * Other condition(s) that in the opinion of the investigator might compromise the objectives of the study