Unmanned Aerial Vehicle (UAV) equipped with Mobile Edge Computing (MEC) server has become a promising solution for on-demand service provisioning in Airborne Maneuvering Networks (AMNs). However, it remains constrained by severe multi-user interference and limited spectral resources. This work investigates a non-orthogonal multiple access-enabled MEC framework in AMNs to address spectrum limitations and support concurrent access for multiple Ground Terminals (GTs), where GTs are multiplexed in the power domain and decoded via successive interference cancellation at the UAV. An energy minimization problem is formulated to jointly optimize UAV flight trajectory, task offloading decisions, and power allocation. To address the resulting non-convex energy minimization problem, a hybrid optimization framework that integrates Proximal Policy Optimization (PPO) with convex programming is proposed. Specifically, the deep reinforcement learning component jointly learns the UAV trajectory, binary task offloading strategy, and uplink power control under dynamic network conditions. In parallel, a convex optimization module efficiently computes the UAV’s flight time allocation to minimize propulsion energy. Simulation results demonstrate that the proposed PPO-driven approach significantly reduces total energy consumption compared to conventional baselines, validating its effectiveness for energy-efficient MEC in UAV-based AMNs.