Users often write reviews on different themes involving linguistic structures with complex sentiments. The sentiment polarity of a word can be different across themes. Moreover, contextual valence shifters may change sentiment polarity depending on the contexts that they appear in. Both challenges cannot be modeled effectively and explicitly in traditional sentiment analysis. Studying both phenomena requires multi-theme sentiment analysis at the word level, which is very interesting but significantly more challenging than overall polarity classification. To simultaneously resolve the multi-theme and sentiment shifting problems, we propose a data-driven framework to enable both capabilities: (1) polarity predictions of the same word in reviews of different themes, and (2) discovery and quantification of contextual valence shifters. The framework formulates multi-theme sentiment by factorizing the review sentiments with theme/word embeddings and then derives the shifter effect learning problem as a logistic regression. The improvement of sentiment polarity classification accuracy demonstrates not only the importance of multi-theme and sentiment shifting, but also effectiveness of our framework. Human evaluations and case studies further show the success of multi-theme word sentiment predictions and automatic effect quantification of contextual valence shifters.