Sorafenib Tosylate and Gemcitabine Hydrochloride in Treating Patients With Recurrent Epithelial Ovarian Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed epithelial ovarian cancer or primary peritoneal cancer that has recurred or is refractory to initial therapy; patients must have received platinum-based chemotherapy before entry into this protocol * Patients who have recurred and are platinum-sensitive (treatment free interval greater than 12 months) must have been re-treated with platinum-based chemotherapy prior to entry into this protocol * Patients may have received no more than three prior chemotherapy regimens (e.g. initial chemotherapy and two regimens for subsequent relapses) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan; if measurable disease is in a radiated site, there must be evidence of disease progression in that lesion post radiation * Life expectancy of greater than 12 weeks * ECOG performance status =\<1 (Karnofsky \>= 70%) * Leukocytes \>= 3,000/uL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) =\< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * The effects of BAY 43-9006 on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because raf kinase inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, 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 * Ability to understand and the willingness to sign a written informed consent document * Patients who are on warfarin anticoagulation are allowed to participate as long as they fit the following 4 criteria: * They are therapeutic on a stable warfarin dose * Their INR target range is no greater than 3 * They are monitored with weekly INR, PT and PTT testing * They have no active bleeding or pathological condition that carries high risk of bleeding * Pregnant women are excluded from this study because BAY 43-9006 is a kinase inhibitor agent with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with BAY 43-9006, breastfeeding should be discontinued if the mother is treated with BAY 43-9006 Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy, hormonal or biologic therapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients with borderline tumours or tumours of low malignant potential * Patients with current bowel obstruction * Patients with previous radiotherapy to \> 30% of bone marrow irradiated in target volume and/or radiotherapy within 4 weeks of study treatment; palliative radiation is allowed within 4 weeks of treatment, after discussion with the Principal Investigator * Patients may not be receiving any other investigational agents concurrently or within 4 weeks; patients who have previous exposure to a raf-kinase inhibitor are excluded * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events * History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006 or other agents used in the study * Patients may not have had prior gemcitabine chemotherapy * No concurrent use of itraconazole, ketoconazole, ritanovir, or grapefruit juice * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with BAY 43-9006; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated