Using a fully vectorial numerical method based on the transformation optics formalism, we analyzed the effect of resonant coupling between the core and cladding modes in twisted, elliptical core fibers. Our rigorous simulations revealed the existence of a much richer resonance spectrum than that predicted by simplified perturbation approaches. This effect is caused by the appearance of even harmonics in the angular field distribution of higher-order cladding modes due to their interaction with the fiber core with two-fold symmetry. We also analyzed the dependence of the polarization state of the core modes upon the twist rate and wavelength. We demonstrated the effect of the resonant-polarization perturbation of the core modes, which is especially visible for the couplings between circularly polarized core modes and cladding modes of opposite handedness.