I. To observe and record anti-tumor activity. (Phase I) II. To determine overall survival (OS), objective response rate (complete and partial responses), clinical benefit rate (response + stable disease), CA-125 reduction (percentage of patients with CA-125 reduction by >= 50%), and duration of response. (Phase IIb) III. To assess the impact of the combination of atezolizumab, SGI-110, and CDX-1401 on anti-tumor immune responses. (Phase IIb) IV. To assess the impact of SGI-110 on NY-ESO-1 expression in tumor tissue. (Phase IIb) V. To assess toxicities associated with the combination cohorts (2 and 3), as there is little human experience with these combinations. (Phase IIb)