We show that coherent interaction between two sets of multiple resonances leads to exotic resonant effects, such as Fano-type resonances, optical analogue of electro-magnetically induced transparency, and avoided crossing between modes, under different coupling regimes. We experimentally demonstrate such resonant effects in a photonic crystal nanofiber cavity using two sets of cavity modes with orthogonal polarizations. The interaction between the modes arises due to intra-cavity polarization mixing. The observed line shapes are reproduced using a multiple-mode interaction model. Such spectral characteristics may further enhance the capabilities of the nanofiber cavity as a fiber-in-line platform for nanophotonics and quantum photonics applications.