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The Internet of Things (IoT) has promoted emerging applications that require massive device collaboration, heavy computation, and stringent latency. Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) systems can provide flexible services for user devices (UDs) with wide coverage. The optimization of both latency and energy consumption remains a critical yet challenging task due to the inherent trade-off between them. Joint association, offloading, and computing resource allocation are essential to achieving satisfying system performance. However, these processes are difficult due to the highly dynamic environment and the exponentially increasing complexity of large-scale networks. To address these challenges, we introduce a carefully designed cost function to balance the latency and the energy consumption, formulate the joint problem into a partially observable Markov decision process, and propose two multi-agent deep-reinforcement-learning-based schemes to tackle the long-term problem. Specifically, the multi-agent proximal policy optimization (MAPPO)-based scheme uses centralized learning and decentralized execution, while the closed-form enhanced multi-armed bandit (CF-MAB)-based scheme decouples association from offloading and computing resource allocation. In both schemes, UDs act as independent agents that learn from environmental interactions and historic decisions, make decision to maximize its individual reward function, and achieve implicit collaboration through the reward mechanism. The numerical results validate the effectiveness and show the superiority of our proposed schemes. The MAPPO-based scheme enables collaborative agent decisions for high performance in complex dynamic environments, while the CF-MAB-based scheme supports independent rapid response decisions.