In scenarios where ground-based cloud computing infrastructure is unavailable, unmanned aerial vehicles (UAVs) act as mobile edge computing (MEC) servers to provide on-demand computation services for ground terminals. To address the challenge of jointly optimizing task scheduling and UAV trajectory under limited resources and high mobility of UAVs, this paper presents PER-MATD3, a multi-agent deep reinforcement learning algorithm with prioritized experience replay (PER) into the Centralized Training with Decentralized Execution (CTDE) framework. Specifically, PER-MATD3 enables each agent to learn a decentralized policy using only local observations during execution, while leveraging a shared replay buffer with prioritized sampling and centralized critic during training to accelerate convergence and improve sample efficiency. Simulation results show that PER-MATD3 reduces average task latency by up to 23%, improves energy efficiency by 21%, and enhances service coverage compared to state-of-the-art baselines, demonstrating its effectiveness and practicality in scenarios without terrestrial networks.