Efficient data offloading plays a pivotal role in computational-intensive platforms as data rate over wireless channels is fundamentally limited. On top of that, high mobility adds an extra burden in vehicular edge networks (VENs), bolstering the desire for efficient user-centric solutions. Therefore, unlike the legacy inflexible network-centric approach, this paper exploits a software-defined flexible, open, and programmable networking platform for an efficient user-centric, fast, reliable, and deadline-constrained offloading solution in VENs. In the proposed model, each active vehicle user (VU) is served from multiple low-powered access points (APs) by creating a noble virtual cell (VC). A joint node association, power allocation, and distributed resource allocation problem is formulated. As centralized learning is not practical in many real-world problems, following the distributed nature of autonomous VUs, each VU is considered an edge learning agent. To that end, considering practical location-aware node associations, a joint radio and power resource allocation non-cooperative stochastic game is formulated. Leveraging reinforcement learning's (RL) efficacy, a multi-agent RL (MARL) solution is proposed where the edge learners aim to learn the Nash equilibrium (NE) strategies to solve the game efficiently. Besides, real-world map data, with a practical microscopic mobility model, are used for the simulation. Results suggest that the proposed user-centric approach can deliver remarkable performances in VENs. Moreover, the proposed MARL solution delivers near-optimal performances with approximately 3% collision probabilities in case of distributed random access in the uplink.