Mobile Edge Computing (MEC) enables latency-critical applications by offloading tasks from resource-limited wireless devices (WDs) to edge servers. However, optimal task offloading and resource allocation remain challenging under dynamic wireless channels and diverse task demands. This paper presents a two-step adaptive solution that combines deep neural networks (DNN) and projected gradient descent. A DNN first predicts binary offloading decisions from real-time channel conditions. Conditioned on these decisions, we solve a constrained optimization problem to determine task partitioning and CPU allocation that minimize the weighted sum delay. To enable rapid adaptation to new task scenarios, we embed meta-learning into DNN training. Simulation results show that our method achieves low delay and strong generalization in multi-user, multi-server MEC environments.