Internet-of-Things (IoT) technology has received much attention due to its great potential to interconnect billions of devices in a broad range of applications. IoT networks can provide high-quality services for a large number of users and smart objects. On the other hand, massive connectivity in IoT networks brings problems associated with spectral congestion. This issue can be solved by applying cognitive radio (CR) and non-orthogonal multiple access (NOMA) techniques. In this respect, this paper studies the performance of cooperative CR-NOMA enabled IoT networks over a generalized $\alpha - \mu $ fading channel model. Closed-form analytical expressions of the end-to-end outage probability (OP) for the secondary NOMA users are derived using the Meijer’s G-function with a consideration of the impacts of the interference temperature constraint, primary interference, residual hardware impairments and imperfect successive interference cancellation. Moreover, to acquire some useful insights on the system performance, asymptotic closed-form OP expressions are provided. Additionally, the impact of $\alpha $ and $\mu $ fading parameters on the outage performance is examined and, as a result, it is concluded that the system performance sufficiently improves as $\alpha $ and/or $\mu $ increase. Furthermore, the outage performance of the proposed system model is shown to outperform that of an identical IoT network operating on orthogonal multiple access. Finally, the provided closed-form OP expressions are validated with Monte Carlo simulations.