Exciton intervalley scattering, annihilation, relaxation dynamics, and diffusive transport in monolayer transition metal dichalcogenides are central to the functionality of devices based on them. Here, these properties in a large-size exfoliated high-quality monolayer MoSe 2 are addressed directly using heterodyned transient grating spectroscopy at room temperature. While the free exciton population is found to be long-lived (≈230 ps), an extremely fast intervalley scattering (≤170 fs) is observed, leading to a negligible valley polarization, consistent with steady state photoluminescence measurements and theoretical calculation. The exciton population decay shows an appreciable contribution from the exciton-exciton annihilation, with an annihilation rate of ≈0.01 cm 2 s −1. The annihilation process also leads to a significant distortion of the transient grating evolution. Taking this distortion into account, consistent exciton diffusion constants D ≈ 1.4 cm 2 s −1 are found by a model simulation in the excitation density range of 10 11-10 12 cm −2. The presented results highlight the importance of correctly considering the many-body annihilation processes to obtain a pronounced understanding of the excitonic properties of monolayer transition metal dichalcogenides.