This article investigates the energy efficiency issue in non-orthogonal multiple access (NOMA)-enhanced Internet-of-Things (IoT) networks, where a mobile unmanned aerial vehicle (UAV) is exploited as a flying base station to collect data from ground devices via the NOMA protocol. With the aim of maximizing network energy efficiency, we formulate a joint problem of UAV deployment, device scheduling and resource allocation. First, we formulate the joint device scheduling and spectrum allocation problem as a three-sided matching problem, and propose a novel low-complexity near-optimal algorithm. We also introduce the novel concept of `exploration into the matching game for further performance improvement. By algorithm analysis, we prove the convergence and stability of the final matching state. Second, in an effort to allocate proper transmit power to IoT devices, we adopt the Dinkelbachs algorithm to obtain the optimal power allocation solution. Furthermore, we provide a simple but effective approach based on disk covering problem to determine the optimal number and locations of UAVs stop points to ensure that all IoT devices can be fully covered by the UAV via line-of-sight (LoS) links for the sake of better channel condition. Numerical results unveil that: i) the proposed joint UAV deployment, device scheduling and resource allocation scheme achieves much higher EE compared to predefined stationary UAV deployment case and fixed power allocation scheme, with acceptable complexity; and ii) the UAV-aided IoT networks with NOMA greatly outperforms the OMA case in terms of number of accessed devices.