The Peccei-Quinn (PQ) mechanism not only acts as an explanation for the absence of strong charge parity ($CP$) violation but also can play a main role in the solution to other open questions in particle physics and cosmology. Here we consider a model that identifies the PQ symmetry as a common thread in the solution to the strong $CP$ problem, the generation of radiative Dirac neutrino masses and the origin of a multicomponent dark sector. Specifically, scotogenic neutrino masses arise at one-loop level with the lightest fermionic mediator field acting as the second dark matter (DM) candidate thanks to the residual ${Z}_{2}$ symmetry resulting from the PQ symmetry breaking. We perform a phenomenological analysis addressing the constraints coming from the direct searches of DM, neutrino oscillation data and charged lepton flavor violating (LFV) processes. We find that the model can be partially probed in future facilities searching for weakly interacting massive particles and axions, and accommodates rates for rare leptonic decays that are within the expected sensitivity of upcoming LFV experiments.