This paper considers a single-input-multiple-output non-orthogonal multiple access enabled vehicular communication system, and investigates its secrecy performance over time-selective fading and channel estimation errors. We formulate two scenarios considering the decoding ability at eavesdropper, viz., 1) Scenario I: when it has sufficient decoding capability, and 2) Scenario II: when its decoding capability can be the same as the legitimate vehicles. Under such a realistic system setup, we derive the secrecy outage probability (SOP) and ergodic secrecy capacity expressions for both legitimate vehicles and the overall system under both Scenarios I and II over Nakagami- m fading channels. We then analyze the asymptotic SOP limits of both legitimate vehicles under Scenarios I and II, by formulating cases based on the average transmit signal-to-noise ratio and average channel gains associated with the main links and wiretap link. From the asymptotic analysis under these cases, it is observed that both legitimate vehicles do not achieve any secrecy diversity order even after leveraging the benefits of fading severity parameters and multiple antennas. We also formulate several special cases of interest to reveal some more insightful information about the system's secrecy performance. Finally, we corroborate our analytical and theoretical findings via simulation results.