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 an…