This paper investigates the physical layer security (PLS) of non-orthogonal multiple access (NOMA)-enabled overlay cognitive radio networks (NOMA-OCRNs), considering multiple non-colluding eavesdroppers. Here PLS is evaluated in terms of: (i) secrecy outage probability (SOP) of primary user (PU) and secondary user (SU) and (ii) system SOP (SSOP), system secrecy throughput (SST) and secrecy energy efficiency (SEE) of the network. Residual hardware impairments arising from non-ideal hardware and imperfect successive interference cancellation conditions are considered. Firstly, we derive new analytical expressions for the SOPs of PU and SU. Numerical evaluation results show that both PU as well as SU suffer very high SOPs that tend to unity in the high transmit power region. Further, RHI and i-SIC have a significant impact on the secrecy performance. To improve the PLS performance, we propose a jammingassisted framework and develop novel analytical models for determining the SOPs of PU and SU. We derive the asymptotic SOP expressions as well. Detailed analytical and simulation results are presented to demonstrate that the proposed jamming-assisted framework leads to a significant reduction of the SOPs of both PU and SU while exhibiting considerable enhancement of SST and SEE of the network compared to the no-jammer scenario. In the final part of this paper, we utilize a deep learning framework for the precise and fast prediction of the SOPs of PU and SU, that can replace complex mathematical modeling.INDEX TERMS Overlay cognitive radio networks, Non-orthogonal multiple access, Physical layer security, Multiple eavesdroppers, Residual hardware impairments, Performance analysis.