In this paper, in order to reduce the energy consumption and time of data transmission, the non-orthogonal multiple access (NOMA) and mobile edge caching technologies are jointly considered in mobile edge computing (MEC) networks. As for the cache-assisted vehicular NOMA–MEC networks, a problem of minimizing the energy consumed by vehicles (mobile devices, MDs) is formulated under time and resource constraints, which jointly optimize the computing resource allocation, subchannel selection, device association, offloading and caching decisions. To solve the formulated problem, we develop an effective joint computation offloading and task-caching algorithm based on the twin-delayed deep deterministic policy gradient (TD3) algorithm. Such a TD3-based offloading (TD3O) algorithm includes a designed action transformation (AT) algorithm used for transforming continuous action space into a discrete one. In addition, to solve the formulated problem in a non-iterative manner, an effective heuristic algorithm (HA) is also designed. As for the designed algorithms, we provide some detailed analyses of computation complexity and convergence, and give some meaningful insights through simulation. Simulation results show that the TD3O algorithm could achieve lower local energy consumption than several benchmark algorithms, and HA could achieve lower consumption than the completely offloading algorithm and local execution algorithm.