In this paper, we study an unmanned aerial vehicle (UAV)-aided non-orthogonal multiple access (NOMA) multi-way relaying networks (MWRNs). Multiple terrestrial users aim to exchange their mutual information via an amplify-and-forward (AF) UAV relay. Specifically, the realistic assumption of the residual hardware impairments (RHIs) at the transceivers is taken into account. To evaluate the performance of the considered networks, we derive the analytical expressions for the achievable sum-rate (ASR). In addition, we carry out the asymptotic analysis by invoking the affine expansion of the ASR in terms of \emph{high signal-to-noise ratio (SNR) slope} and \emph{high SNR power offset}. Numerical results show that: 1) Compared with orthogonal multiple access (OMA), the proposed networks can significantly improve the ASR since it can reduce the time slots from $\left[ {\left( {M - 1} \right)/2} \right] + 1$ to 2; and 2) RHIs of both transmitter and receiver have the same effects on the ASR of the considered networks.