Mobile Edge Computing (MEC) has emerged as an effective solution to support latency-sensitive and computationintensive applications in Internet of Things (IoT) environments. However, efficient task offloading remains a challenging problem due to dynamic network conditions, heterogeneous device capabilities, and limited edge resources. Existing approaches, including heuristic methods, supervised learning, and deep learning models, cannot effectively adapt to dynamic network conditions, heterogeneous device capabilities, and multi-device resource contention. Single-agent reinforcement learning methods also fail to scale in environments where multiple devices compete for shared edge resources. To address these limitations, this paper proposes a Graph-Attention Multi-Agent Proximal Policy Optimization (GA-MAPPO) framework for intelligent and energy-efficient task offloading in MEC systems. In the proposed framework, each IoT device operates as an independent reinforcement learning agent, while a graph attention mechanism captures the relationships among devices, edge servers, and communication links. Proximal Policy Optimization ensures stable and efficient policy updates, allowing the system to adapt to changing workloads and network conditions. The multi-agent architecture supports collaborative decision-making, improving scalability and resource utilization across devices. Experimental results show that GA-MAPPO achieves 94% classification accuracy in offloading decisions and outperforms existing methods including DQN-based, PPO-based, MARL, and GNNbased approaches in terms of latency reduction, energy efficiency, and resource utilization. These results confirm that the proposed framework provides a scalable and adaptive solution for task offloading in next-generation MEC systems.