Non-orthogonal multiple access (NOMA) system can meet the demands of ultra-high data rate, ultra-low latency, ultra-high reliability and massive connectivity of user devices (UE). However, the performance of the NOMA system may be deteriorated by the hardware impairments. In this paper, the joint effects of in-phase and quadrature-phase imbalance (IQI) and imperfect successive interference cancellation (ipSIC) on the performance of two-way relay cooperative NOMA (TWR C-NOMA) networks over the Rician fading channels are studied, where two users exchange information via a decode-and-forward (DF) relay. In order to evaluate the performance of the considered network, analytical expressions for the outage probability of the two users, as well as the overall system throughput are derived. To obtain more insights, the asymptotic outage performance in the high signal-to-noise ratio (SNR) region and the diversity order are analysed and discussed. Throughout the paper, Monte Carlo simulations are provided to verify the accuracy of our analysis. The results show that IQI and ipSIC have significant deleterious effects on the outage performance. It is also demonstrated that the outage behaviours of the conventional OMA approach are worse than those of NOMA. In addition, it is found that residual interference signals (IS) can result in error floors for the outage probability and zero diversity orders. Finally, the system throughput can be limited by IQI and ipSIC, and the system throughput converges to a fixed constant in the high SNR region.