In this paper, a multi-vehicle multi-task non-orthogonal multiple access (NOMA) assisted mobile edge computing (MEC) system with passive eavesdropping vehicles is investigated. To heighten the performances of edge vehicles, we propose a vehicle grouping pairing method, which utilizes vehicles near the MEC to assist edge vehicles as full-duplex relays. For promoting transmission security, we employ artificial noise to interrupt eavesdropping vehicles. Furthermore, we derive the approximate expression of the secrecy outage probability of the system. The combined optimization of vehicle task division, power allocation, and transmit beamforming is formulated to minimize the total delay of task completion for edge vehicles. Then, we design a power allocation and task scheduling algorithm based on the genetic algorithm to solve the mixed-integer non-linear programming problem. Numerical results demonstrate the superiority of our proposed scheme in terms of system security and transmission delay.