Erlotinib Plus Carboplatin and Paclitaxel in Ovarian Carcinoma

Inclusion Criteria: * Patients with a histologic diagnosis of primary peritoneal carcinoma, fallopian tube epithelial ovarian carcinoma, Stage III with either greater than 1 cm (suboptimal) residual disease following initial surgery, or Stage IV; all patients must either have had appropriate surgery for ovarian, fallopian tube or peritoneal carcinoma with appropriate tissue available for histologic evaluation to confirm diagnosis and stage or must be unresectable at time of diagnosis (to be determined by gynecological oncologist); cytology alone is not adequate * Patients with the following histologic epithelial cell types are eligible: Serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's Tumor, or adenocarcinoma not otherwise specified (NOS) * Patients must begin chemotherapy on this study no more than twelve weeks postoperatively * Patients must not have received chemotherapy within five years prior to enrollment * ECOG performance status =\< 2 (Karnofsky \>= 60%) * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin =\< 1.5 x institutional upper limit of normal * AST(SGOT)/ALT(SGPT) =\< 2.5 x institutional upper limit of normal * Creatinine =\< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Neuropathy (sensory and motor) =\< CTC grade 1 * No medical contraindications to planned regimen * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had courses of chemotherapy within the five years prior to entering the study * Patients may not be receiving any other investigational agents * 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 OSI-774 or other agents used in the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because OSI-774 has 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 OSI-774, breastfeeding should be discontinued if the mother is treated with OSI-774; these potential risks may also apply to other agents used in this study * Because patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with OSI-774 or other agents administered during the study; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated