Accurate user interest modeling is important for news recommendation. Most existing methods for news recommendation rely on implicit feedbacks like click for inferring user interests and model training. However, click behaviors usually contain heavy noise, and cannot help infer complicated user interest such as dislike. Besides, the feed recommendation models trained solely on click behaviors cannot optimize other objectives such as user engagement. In this paper, we present a news feed recommendation method that can exploit various kinds of user feedbacks to enhance both user interest modeling and model training. We propose a unified user modeling framework to incorporate various explicit and implicit user feedbacks to infer both positive and negative user interests. In addition, we propose a strong-to-weak attention network that uses the representations of stronger feedbacks to distill positive and negative user interests from implicit weak feedbacks for accurate user interest modeling. Besides, we propose a multi-feedback model training framework to learn an engagement-aware feed recommendation model. Extensive experiments on a real-world dataset show that our approach can effectively improve the model performance in terms of both news clicks and user engagement.