We compute the magnetoelectric conductivity of a semimetal hosting an ideal gapped nodal ring (GNR) in three distinct planar-Hall configurations, in the simultaneous presence of an external electric field E, a magnetic field B, and a strain-induced axial pseudomagnetic field B₅. The latter arises from a nonuniform lattice deformation and couples to antipodal points on the toroidal Fermi surface with opposite signs, reflecting its chiral nature. Extending our earlier analysis to include B₅, we demonstrate how its vortex-like field lines — co-aligned with the Berry curvature (BC) and orbital magnetic moment (OMM) — imprint qualitatively distinct signatures on the conductivity tensor. In particular, this alignment causes the dot product of B₅ with the BC or OMM-induced quantities to be angle-independent on the Fermi surface, generating a nonvanishing integral linear-in-B₅, which is not possible for isotropic nodal points harbouring BC-monopoles. We show that a part of the planar-Hall conductivity in the first set-up remains completely immune to strain, providing a strain-insensitive internal reference for topological transport. Our explicit analytical expressions offer concrete and experimentally-testable predictions for identifying strain-induced signatures in transport measurements on GNR materials.