Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) and data collection (DC) have been popular research issues. Different from existing works that consider MEC and DC scenarios separately, this paper investigates a multi-UAV-assisted joint MEC-DC system. Specifically, we formulate a joint optimization problem to minimize the MEC latency and maximize the collected data volume. This problem can be classified as a non-convex mixed integer programming problem that exhibits long-term optimization and dynamics. Thus, we propose a deep reinforcement learning-based approach that jointly optimizes the UAV movement, user transmit power, and user association in real time to solve the problem efficiently. Specifically, we reformulate the optimization problem into an action space-reduced Markov decision process (MDP) and optimize the user association by using a two-phase matching-based association (TMA) strategy. Subsequently, we propose a soft actor-critic (SAC)-based approach that integrates the proposed TMA strategy (SAC-TMA) to solve the formulated joint optimization problem collaboratively. Simulation results demonstrate that the proposed SAC-TMA is able to coordinate the two subsystems and can effectively reduce the system latency and improve the data collection volume compared with other benchmark algorithms.