In this paper, a cooperative non-orthogonal multiple access (NOMA) system is studied for the Internet-of-Things (IoT) in which a master node intends to serve multiple client nodes. The adaptive transmission strategy is proposed at the relay node, i.e., the relay can be half-duplex (HD) and/or full duplex (FD). In practical terms, numerous low-cost devices are deployed in such IoT systems and it exhibits degraded performance due to hardware imperfections. In particular, the effects of hardware impairments in the NOMA users are investigated. Specifically, the closed-form expressions are derived for the outage probability. Moreover, the ergodic capacity is also analysed. This study also comparatively analyzes the orthogonal multiple access (OMA) and NOMA with HD and/or FD relaying. The numerical results are corroborated through Monte Carlo simulations.