In the era of rapid technological advancement, Mobile Edge Computing (MEC) has become essential for supporting latency-sensitive applications such as IoT, autonomous driving, and smart cities. However, efficient resource allocation remains a challenge due to the dynamic nature of MEC environments. This study proposes an advanced Multi-Agent Reinforcement Learning (MARL) framework combined with a lightweight neural network, LtNet, to optimize task offloading and resource management in MEC. The MARL framework allows each device to learn its optimal offloading strategy, while LtNet enhances computational efficiency using H-Swish activation and selective Squeeze-and-Excitation modules. Experimental results demonstrate that the proposed methods achieve a 12-22% reduction in task completion time, a 5-8% decrease in energy consumption, and consistently high resource utilization, making them highly effective in managing dynamic MEC environments.