The main purpose of this research study is to collect information to learn how effective erlotinib (tarceva) is in combination with either bevacizumab or sulindac in treating patients with squamous cell carcinoma of the head and neck. Erlotinib and bevacizumab are targeted therapy drugs that can control tumor growth by targeting specific abnormalities sometimes found on cancer cells. Erlotinib targets epidermal growth factor receptor (EGFR), and bevacizumab targets vascular endothelial growth factor (VEGF). Sulindac is a non-steroidal anti-inflammatory drug (NSAID) that can block G protein-coupled receptor which laboratory evidence shows is associated with both cancer cell growth and EGFR activity. The bevacizumab being administered in this study is not a commercially marketed formulation of the drug. Previous research with head and neck cancer suggest that erlotinib alone has some anti-cancer activity. This research study is designed to see how well erlotinib works in combination with bevacizumab or sulindac in head and neck cancer.