We theoretically propose and investigate an optical analogue of neutrino oscillations in a pair of vertically displaced binary waveguide arrays with longitudinally modulated effective refractive index. Optical propagation is modeled through coupled-mode equations, which in the continuous limit converge to two coupled Dirac equations for fermionic particles with different mass states, analogously to neutrinos. In addition to simulating neutrino oscillation in the noninteracting regime, our optical setting enables us to explore neutrino interactions in extreme regimes that are expected to play an important role in massive supernova stars. In particular, we predict the quenching of neutrino oscillations and the existence of topological defects, i.e., neutrino solitons, which in our photonic simulator should be observable as excitation of optical gap solitons propagating along the binary arrays at high excitation intensities