Sentiment and emotion, which correspond to long-term and short-lived human feelings, are closely linked to each other, leading to the fact that sentiment analysis and emotion recognition are also two interdependent tasks in natural language processing (NLP). One task often leverages the shared knowledge from another task and performs better when solved in a joint learning paradigm. Conversational context dependency, multi-modal interaction, and multi-task correlation are three key factors that contribute to this joint paradigm. However, none of the recent approaches have considered them in a unified framework. To fill this gap, we propose a multi-modal, multi-task interactive graph attention network, termed M3GAT, to simultaneously solve the three problems. At the heart of the model is a proposed interactive conversation graph layer containing three core sub-modules, which are: (1) local-global context connection for modeling both local and global conversational context, (2) cross-modal connection for learning multi-modal complementary and (3) cross-task connection for capturing the correlation across two tasks. Comprehensive experiments on three benchmarking datasets, MELD, MEISD, and MSED, show the effectiveness of M3GAT over state-of-the-art baselines with the margin of 1.88%, 5.37%, and 0.19% for sentiment analysis, and 1.99%, 3.65%, and 0.13% for emotion recognition, respectively. In addition, we also show the superiority of multi-task learning over the single-task framework.