This paper investigates the impact of residual transceiver hardware impairments (RTHIs) on cooperative non-orthogonal multiple access (NOMA) networks, where generic $\alpha -\mu $ fading channel is considered. To be practical, imperfect channel state information (CSI) and imperfect successive interference cancellation (SIC) are taken into account. More particularly, two representative NOMA scenarios are proposed, namely non-cooperative NOMA and cooperative NOMA. For the non-cooperative NOMA, the base station (BS) directly performs NOMA with all users. For the cooperative NOMA, the BS communicates with NOMA users with the aid of an amplify-and-forward (AF) relay, and the direct links between BS and users are existent. To characterize the performance of the proposed networks, new closed-form and asymptotic expressions for the outage probability (OP), ergodic capacity (EC) and energy efficiency (EE) are derived, respectively. Specifically, we also design the relay location optimization algorithms from the perspectives of minimize the asymptotic OP. For non-cooperative NOMA, it is proved that the OP at high signal-to-noise ratios (SNRs) is a function of threshold, distortion noises, estimation errors and fading parameters, which results in 0 diversity order. In addition, high SNR slopes and high SNR power offsets achieved by users are studied. It is shown that there are rate ceilings for the EC at high SNRs due to estimation error and distortion noise, which cause 0 high SNR slopes and $\infty $ high SNR power offsets . For cooperative NOMA, similar results can be obtained, and it also demonstrates that the outage performance of cooperative NOMA scenario exceeds the non-cooperative NOMA scenario in the high SNR regime.