The proliferation of computation-intensive applications, such as generative artificial intelligence and low-altitude economy services, demands mobile edge computing (MEC) systems that are both energy-efficient and adaptable to highly dynamic workloads. However, conventional MEC architectures rely on fixed-position antennas with limited spatial flexibility and rigid single-slot task execution models, which fail to accommodate bursty traffic and time-varying channels. To address these challenges, this paper proposes a novel MEC framework empowered by movable antennas (MAs) and task buffering. Unlike traditional approaches, our system enables continuous antenna repositioning to maximize array gains and decouples task generation from immediate execution via buffer queues, allowing for flexible multi-slot scheduling. We formulate a stochastic optimization problem to minimize long-term energy consumption by jointly optimizing receive beamforming, MA positions, and computing resources. Leveraging Lyapunov optimization, we transform the long-term problem into tractable per-slot subproblems and develop an efficient alternating optimization algorithm. Simulation results demonstrate that the proposed scheme significantly outperforms the benchmark schemes in terms of energy consumption, while maintaining stable task queues under unpredictable traffic conditions.

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