Electrons in transition-metal dichalcogenides (TMDs) possess valley and spin degrees of freedom, which leads to rich exciton and exciton-polariton physics with nontrivial scattering dynamics and enhanced nonlinearities, presenting a key mechanism for photonic devices. Yet, existing descriptions of bosonization and polariton interactions in TMD-based systems overlook the valley degree of freedom as well as the various particles spins combinations. In this work, we derive a nonequilibrium field-theory approach in the path integral formalism that allows to track all the polariton nonlinearities in the strong coupling regime. We demonstrate that, when all the bright and dark exciton species are considered, the TMD monolayer-based polariton systems feature sixteen different nonlinear contributions due to interactions and even more saturation-related terms. Strikingly, while the interactions of excitons within one valley are overall dominant, we show that the interaction constant corresponding to the scattering of spin-dark and bright excitons is much larger than that for bright excitons alone, indicating a possibly much higher contribution to the blueshift from spin-dark excitons than from bright intravalley excitons.