We present Floquet theory based predictions and electrically detected magnetic resonance (EDMR) experiments to elucidate the nature of multiphoton magnetic resonance shifts of charge-carrier spin states in films of the perdeuterated π-conjugated polymer poly[2-(2-ethylhexyloxy-d17)-5-methoxy-d3-1,4-phenylenevinylene-d4] (d-MEH-PPV) under strong magnetic resonant drive conditions (radiation amplitude B1 comparable to Zeeman field B0). Room-temperature, continuous-wave EDMR experiments on d-MEH-PPV-based, electroluminescent, bipolar-injection diodes [i.e., organic light-emitting diodes (OLEDs)] confirm the ability of a nonperturbative numerical method to make quantitative predictions of two-photon resonance shifts in such devices. Additional numerical simulations show that the two-photon resonance shift with increasing power is nearly the same under both linearly and circularly polarized drive, in contrast to the one-photon shift, which only occurs under conditions of noncircularly polarized drive. We therefore treat the Floquet Hamiltonian analytically using arbitrary amplitudes of the co- and counterrotating components of the radiation field to gain insight into the nature of the polarization dependence of multiphoton resonance shifts. The results show that multiphoton resonance shifts depend on both the co- and counterrotating components of an arbitrarily polarized drive field, whereas the one-photon shift depends only on the counterrotating component.