Ensuring secure and efficient multi-user (MU) transmission is critical for vehicular communication systems. Chaos-based modulation schemes have garnered considerable interest due to their benefits in physical layer security. However, most existing MU chaotic communication systems, particularly those based on non-coherent detection, suffer from low spectral efficiency due to reference signal transmission, and limited user connectivity under orthogonal multiple access (OMA). While non-orthogonal schemes, such as sparse code multiple access (SCMA)-based DCSK, have been explored, they face high computational complexity and inflexible scalability due to their fixed codebook designs. This paper proposes a deep learning-assisted power domain non-orthogonal multiple access chaos shift keying (DL-NOMA-CSK) system for vehicular communications. A deep neural network (DNN)-based demodulator is designed to learn intrinsic chaotic signal characteristics during offline training, thereby eliminating the need for chaotic synchronization or reference signal transmission. The demodulator employs a dual-domain feature extraction architecture that jointly processes the time-domain and frequency-domain information of chaotic signals, enhancing feature learning under dynamic channels. The DNN is integrated into the successive interference cancellation (SIC) framework to mitigate error propagation issues. Theoretical analysis and extensive simulations demonstrate that the proposed system achieves superior performance in terms of spectral efficiency (SE), energy efficiency (EE), bit error rate (BER), security, and robustness, while maintaining lower computational complexity compared to traditional MU-DCSK and existing DL-aided schemes. These advantages validate its practical viability for secure vehicular communications.