The microscopic interactions and dynamics probed by third-order Raman spectroscopy in an atomic liquid (Xe) are explored within the Drude oscillator model, both numerically and analytically. Many-body polarization effects reduce the coefficient of the effective dipole-induced-dipole tensor. The isotropic part of the effective dipole-induced-dipole tensor arises primarily from the three-body interaction and is short-ranged. With an isotropic sample, the Raman response in any polarization geometry can be rigorously decomposed into an isotropic component and an anisotropic component, which primarily measure the strength and evolution of the two-body and three-body interactions, respectively. An interesting result from our analysis is the derivation of the standard mode-coupling equation for the intermediate scattering function and the mode-coupling equation for the bilinear density mode using Gaussian factorization of the memory kernel and the mean spherical approximation of the direct correlation function. The initial moment expansion along with the Gaussian factorization scheme allows us to predict the temporal profile of the Raman response function with reasonable accuracy. Furthermore, the Kirkwood superposition scheme approximates the Raman correlation function with pair distribution functions and time correlation functions and allows us to predict the ratio of the pair, three-particle, and four-particle contributions. These results, though obtained for Xe, are generally helpful in interpreting third-order spectroscopies of other liquids.