Phase II Randomized Trial of the Combination of Cetuximab and Sorafenib or Single Agent Cetuximab

Inclusion Criteria: * Patients with recurrent, refractory or metastatic squamous cell carcinoma of oral cavity, oropharynx and larynx, hypopharynx or paranasal sinus, head and neck unknown primary or nasopharyngeal carcinoma WHO type 1; patients with recurrent, refractory or metastatic squamous cell carcinoma of oral cavity, oropharynx and larynx, hypopharynx or paranasal sinus, head and neck unknown primary or nasopharyngeal carcinoma WHO type 1; patients may have had up to 1 prior palliative chemotherapy for recurrent or metastatic disease; please note that chemotherapy given as part of a regimen for curative intent for recurrent disease does not count as "prior chemotherapy;" patients must not presently be candidates for curative therapy * ECOG performance status 0, 1 or 2 * Hemoglobin \>= 9.0/dl * Absolute-neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Total bilirubin =\< 1.5 x ULN * ALT and AST =\< 2.5 x ULN (=\< 5 x ULN for patients with liver involvement) * INR \< 1.5 or a PT and PTT within normal limits * Creatinine =\< 1.5 x ULN * If primary therapy was given for curative intent, at least 4 weeks must have elapsed after completion of primary therapy prior to enrollment on this clinical trial; however, toxicities from prior treatment must have resolved to grade 1 or less * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of the treatment; women of childbearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation (i.e, a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study and for a minimum of 3 months following the last dose of chemotherapy; male subject agrees to use an acceptable method for contraception for the duration of the study and for a minimum of 3 months following the last dose of chemotherapy * Patients must have a measurable disease defined by RECIST criteria * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care; patients or their legal representatives must be able to read, understand and provide informed consent to participate in the trial Exclusion Criteria: * Prior treatment with sorafenib or cetuximab * Patients with active clinically significant infection or with a fever \>= 38.5º C within 3 days of the first scheduled day of protocol treatment * History of prior malignancy within the past 3 years except for curatively treated basal cell carcinoma and squamous cell carcinoma of the skin, CIN or localized prostate cancer with a current PSA \< 1.0 mg/dL on 2 successive evaluations at least 3 months apart, with the most recent evaluation within 4 weeks of study entry * Patients with known hypersensitivity to sorafenib or cetuximab * Prior severe infusion reaction to a monoclonal antibody * History of hand-foot syndrome * Pregnant or lactating; sexually active women of childbearing potential must use an effective method of birth control during the course of the study, in a manner such that risk of failure is minimized * Known untreated brain metastasis; patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis or progression of brain metastasis; patients with treated brain metastasis are eligible for study as long as no evidence of progression of CNS disease; hemorrhagic brain metastases are not allowed on study * Uncontrolled comorbid illness * Patients with HIV who are taking antiretroviral mediations will be excluded because of the potential interactions of anti-retroviral medications with these agent; however, given the potential immune modulating effects of sorafenib, investigators should still be very cautious about placing HIV positive patients on this trial as the effects of these medications on the HIV virus itself are not know * History of allogeneic transplant * Patient has received other investigational drugs within 28 days before enrollment * Cardiac disease: congestive heart failure \> class II NYHA; patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months; significant history of uncontrolled cardiac disease; i.e., uncontrolled hypertension (defined as defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management), uncontrolled congestive heart failure, and cardiomyopathy with decreased ejection fraction will also be excluded from study; cardiac ventricular arrhythmias requiring anti-arrhythmic therapy will also be excluded from study * Thrombotic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months * Pulmonary hemorrhage/bleeding event \> CTCAE grade 2 within 4 weeks of first dose of study drug * Any other hemorrhage/bleeding event \> CTCAE grade 3 within 4 weeks of first dose of study drug * Tumor that invades the carotid artery as shown unequivocally by imaging studies * Serious non-healing wound, ulcer, or bone fracture * Evidence or history of bleeding diathesis or coagulopathy * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug * Use of St. John's Wort or rifampin (rifampicin) * Use of the following medications will not be allowed within 4 weeks prior to enrollment on the study and during the study: ketoconazole, itraconazole, ritonavir, cyclosporine, carbamazepine, phenytoin, phenobarbital; products containing grapefruit juice will not be allowed while on study * Known or suspected allergy to sorafenib or any agent given in the course of this trial * Any malabsorption problem * Known HIV positive patients will be excluded from trial due to the potential immune modulation that these agents may cause