Sorafenib, Docetaxel, and Cisplatin in Treating Patients With Metastatic or Advanced Gastric or Gastroesophageal Junction Cancer

Inclusion Criteria: * Patients must have measurable, histologically confirmed, advanced unresectable or metastatic gastric or GEJ adenocarcinoma; imaging studies must be conducted within 4 weeks of study entry * For patients with GEJ adenocarcinoma, the tumor location should be specified using the Siewert classification used in other NCI-sponsored Phase II studies in these disease sites * Patients must have an ECOG performance status of 0-1 * Patients may have had adjuvant chemotherapy or chemoradiation therapy, with or without 5-Fluorouracil if the treatment was performed more than 6 months before any evidence of recurrent or metastatic disease * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and 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 * Must have the following baseline laboratory values obtained within 2 weeks of registration: * Absolute Granulocyte Count \>= 1,500/mm\^3 * Platelet Count \>= 100,000/mm\^3 * White Blood Count \>= 3,000/mm\^3 * Serum Creatinine \<= 1.5 mg/dl * Total Bilirubin \<= 2.0 mg/dl * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT)/alkaline phosphatase (Alk phos) \<= 2.5 x upper limit of normal * Patients must be able to take oral medication without crushing, dissolving or chewing tablets Exclusion Criteria: * Prior radiotherapy, chemotherapy or investigational therapies, particularly inhibitors of tyrosine Kinases, signal transduction or angiogenesis in the treatment for their recurrent and/or metastatic gastric or GEJ adenocarcinoma * Receiving any other investigational agents * Being pregnant or breast-feeding; all females of childbearing potential must have a blood or urine test within 2 weeks prior to registration to rule out pregnancy * HIV-positive patients receiving combination antiretroviral therapy are excluded from the study because of possible pharmacokinetic interactions with BAY 43-9006 * Brain metastases * History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 * Acute active infection with significant clinical intervention per physician's discretion * Previous or concurrent malignancies are not allowed, except: * Non-melanoma skin cancer and in situ cervical cancer * Treated cancer from which the patient has been continuously disease-free for more than five years * Other uncontrolled intercurrent illnesses including, but not limited to: uncontrolled hypertension, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/addictive disorders that would limit compliance with study requirements * Evidence of bleeding diathesis * Concurrent cytochrome P450 enzyme-inducing anti-epileptic drugs: * Phenytoin * Carbamazepine * Phenobarbital * Rifampin * St. John's Wort