The existing computation and communication (2C) optimization schemes for vehicular edge computing (VEC) networks mainly focus on the physical domain without considering the influence from the social domain. This may greatly limit the potential of task offloading, making it difficult to fully boom the task offloading rate with given power, resulting in low energy efficiency (EE). To address the issue, this letter devotes itself to investigate social-mobility-aware VEC framework and proposes a novel EE-oriented 2C assignment scheme. In doing so, we assume that the task vehicular user (T-VU) can offload computation tasks to the service vehicular user (S-VU) and the road side unit (RSU) by non-orthogonal multiple access (NOMA). An optimization problem is formulated to jointly assign the 2C resources to maximize the system EE, which turns out to be a mixed integer non-convex objective function. To solve the problem, we transform it into separated computation and communication resource allocation subproblems. Dealing with the first subproblem, we propose a social-mobility-aware edge server selection and task splitting algorithm (SM-SSTSA) to achieve edge server selection and task splitting. Then, by solving the second subproblem, the power allocation and spectrum assignment solutions are obtained utilizing a tightening lower bound method and a Kuhn-Munkres algorithm. Finally, we solve the original problem through an iterative method. Simulation results demonstrate the superior EE performance of the proposed scheme.