Capture rates of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta (0νββ) decays of current experimental interest are computed. The corresponding OMC (capture-rate) strength functions have been analyzed in terms of multipole decompositions. The computed low-energy OMC-rate distribution to 76 As is compared with the available data of Zinatulina et al. [Phys. Rev. C 99, 024327 (2019)]. The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The participant nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange G matrix. The Hamiltonian parameters are taken from our earlier work [Jokiniemi et al., Phys. Rev. C 98, 024608 (2018)], except for A = 82 nuclei for which the parameters were determined in this work. Both the OMC and 0νββ decays involve momentum exchanges of the order of 100 MeV and thus future measurements of the OMC strength functions for 0νββ daughter nuclei help trace the in-medium renormalization of the weak axial couplings with the aim to improve the accuracy of the 0νββ-decay nuclear matrix elements.