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Vehicular edge computing (VEC) becomes a promising paradigm for the development of emerging intelligent transportation systems. Nevertheless, the limited resources and massive transmission demands bring great challenges on implementing vehicular applications with stringent deadline requirements. This work presents a non-orthogonal multiple access (NOMA) based architecture in VEC, where heterogeneous edge nodes are cooperated for real-time task processing. We derive a vehicle-to-infrastructure (V2I) transmission model by considering both intra-edge and inter-edge interferences and formulate a cooperative resource optimization (CRO) problem by jointly optimizing the task offloading and resource allocation, aiming at maximizing the service ratio. Further, we decompose the CRO into two subproblems, namely, task offloading and resource allocation. In particular, the task offloading subproblem is modeled as an exact potential game (EPG), and a multi-agent distributed distributional deep deterministic policy gradient (MAD4PG) is proposed to achieve the Nash equilibrium. The resource allocation subproblem is divided into two independent convex optimization problems, and an optimal solution is proposed by using a gradient-based iterative method and KKT condition. Finally, we build the simulation model based on real-world vehicle trajectories and give a comprehensive performance evaluation, which conclusively demonstrates the superiority of the proposed solutions.