As the applications and services within vehicular networking systems become increasingly diverse, vehicles with limited computing resources face challenges in handling these computationally intensive and latency-sensitive tasks. In this paper, we propose an improved Task Offloading Scheduling Strategy based on a Double Deep Q-Network (TOSDDQN) for a dynamic multi-vehicle, multi-edge unit task offloading environment in vehicular networking. This strategy designs communication models and computational models aimed at minimizing the total system overhead in processing tasks. To further protect the privacy of vehicle users, a Distributed Training Algorithm based on Federated Learning (DTAFL) is proposed. Comparative experimental results indicate that, compared to three other task offloading schemes, our approach reduces the average system overhead in processing tasks by 11%–36%.