This clinical trial includes Phase 1 and Phase 2 segments. During the Phase 1 segment, six groups of 6 to 24 patients will be treated with different dose levels of CDX-1401 in combination with either one or both of the immune stimulants (Resiquimod and/or poly-ICLC). This phase of the study will test the safety profile of the vaccine treatment, and will assess which dose to test in future studies. During the Phase 2 segment, 14 patients whose cancer tested positive for the NY-ESO-1 protein in laboratory testing, will receive the study treatment to determine if it has an effect on their cancer. All patients enrolled in either part of the study may continue to receive study treatment until their disease has progressed or until it is necessary to stop the treatment for safety or other reasons. In addition, all patients will be "followed" for 24 months after enrollment in order to collect survival information.