Recent advancements in physics-based character animation leverage deep learning to generate agile and natural motion, enabling characters to execute movements such as backflips, boxing, and tennis. However, reproducing the selection and use of diverse motor skills in dynamic environments to solve complex tasks, as humans do, still remains a challenge. We present a strategy and skill learning approach for physics-based table tennis animation. Our method addresses the issue of mode collapse, where the characters do not fully utilize the motor skills they need to perform to execute complex tasks. More specifically, we demonstrate a hierarchical control system for diversified skill learning and a strategy learning framework for effective decision-making. We showcase the efficacy of our method through comparative analysis with state-of-the-art methods, demonstrating its capabilities in executing various skills for table tennis. Our strategy learning framework is validated through both agent-agent interaction and human-agent interaction in Virtual Reality, handling both competitive and cooperative tasks.