Chemotherapy & Erlotinib in Treating Patients w/ Esophageal or Gastroesophageal Cancer That Cannot Be Removed by Surgery

Inclusion Criteria: * Histologically confirmed esophageal carcinoma (squamous or adenocarcinoma) * Surgically unresectable disease and/or metastatic disease; endoscopic accessibility of the primary tumor is preferred but not a prerequisite * No prior chemotherapy therapy except for neoadjuvant treatment (radiation and/or chemotherapy); prior treatment with EGFR-inhibiting agents is not allowed * Life expectancy \> 12 weeks * Patients must have the ability to take and retain oral medications or have an appropriate percutaneous feeding tube in place * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 (Karnofsky Performance Status (KPS) \>= 50%) * Patients must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria and radiographic imaging performed within 28 days prior to registration * Absolute neutrophil count (ANC) \>= 1500/mL * Platelet count \>= 100,000/mL * Hemoglobin level \>= 10.0 gm/dL * Serum creatinine =\< 1.5 x IULN (institutional upper limits of normal); OR measured creatinine clearance \>= 60 mL/min * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase (SGOT)) or alanine aminotransferase (ALT) (serum glutamic pyruvate transaminase (SGPT)) =\< 2.5 x IULN (unless the liver is involved by tumor, in which case it must be =\< 5.0 x IULN) * Total bilirubin =\< 1.5 x IULN * Provision of written informed consent * Women of childbearing potential (WOCBP) must be willing to practice acceptable methods of birth control to prevent pregnancy; WOCBP are any females who have experienced menarche and who have not undergone surgical sterilization (hysterectomy, bilateral tubal ligation, or bilateral oophorectomy), who are not postmenopausal (defined as amenorrhea \>= 12 consecutive months), or are on hormone replacement therapy; acceptable methods of birth control include oral or hormonal contraceptives and barrier methods (e.g., condom, diaphragm) used in combination with other methods (e.g., spermicide) * Male patients who are capable of fathering a child must avoid doing so while participating in this study through the use of acceptable methods of birth control; this is a precautionary measure because this study involves chemotherapy agents Exclusion Criteria: * Presence of a Kras mutation * Lack of expression of EGFR (tumors that do not have detectable EGFR staining in at least 10% of tumor cells will not be considered EGFR-positive) * Prior treatment with EGFR-inhibiting agents, chemotherapy, or radiotherapy for esophagogastric carcinomas (other than neoadjuvant treatment as noted in inclusion criteria) * Patients must not be receiving any other investigational agents; use of erythropoietin is allowable; secondary prophylaxis with granulocyte colony stimulating factor (G-CSF) (Filgrastim) is allowable * The patient concomitantly uses phenytoin, carbamazepine, barbiturates, rifampicin, phenobarbital, or St. John's wort * Uncontrolled brain metastases * Patients must not have uncontrolled intercurrent illness at the time of registration 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 * Patients must not have current New York Heart Association Class III or IV heart disease * Known human immunodeficiency virus (HIV) infection * Pregnant or breast-feeding women * Patients who have had prior malignancies, except non-melanoma skin cancer (basal or squamous cell carcinoma) are not eligible for this study; unless greater than 5 years has passed since the event * Known severe hypersensitivity to Tarceva * Treatment with a non-approved or investigational drug within 30 days before day 1 of trial treatment * Incomplete healing from previous oncologic or other major surgery * Serum creatinine level greater than Common Toxicity Criteria (CTC) grade 2