Collision-induced light scattering spectra of the inert gases and hydrogen at high densities provide evidence of nonadditive three-body interaction effects, for which a quantitative theory is needed. In this work, we derive and evaluate the three-body polarizability Delta alpha((3)) for interacting molecules with negligible electronic overlap. Our results, based on nonlocal response theory, account for dipole-induced-dipole (DID) interactions, quadrupolar induction, dispersion, and concerted induction-dispersion effects. The contribution of leading order comes from a DID term that scales as alpha(3)d(-6) in the molecular polarizability alpha and a representative distance d between the molecules in a cluster. Quadrupolar induction effects are also large, however, ranging from similar to 35% to 104% of the leading DID terms for equilateral triangular configurations of the species studied in this work, at separations approximately 1 a.u. beyond the van der Waals minima in the isotropic pair potentials. For the same configurations, the dispersion terms range from 2% to 7% of the total Delta<(alpha)over bar>((3)). The dispersion and induction-dispersion contributions are derived analytically in terms of integrals over imaginary frequency, with integrands containing the polarizability alpha(i omega) and the gamma hyperpolarizability. For H, He, and H-2, the integrals have been evaluated accurately by 64-point Gauss-Legendre quadrature; for heavier species, we have developed approximations in terms of static polarizabilities, static hyperpolarizabilities, and van der Waals interaction energy coefficients (C-6 and C-9). In the isotropic interaction-induced polarizability Delta<(alpha)over bar>, the three-body terms are comparable in magnitude to the two-body terms, due to a cancellation of the first-order, two-body DID contributions to Delta<(alpha)over bar>. For the heavier species in this work (Ar, Kr, Xe, N-2, CH4, and CO2) in the configurations studied, the three-body contributions to Delta<(alpha)over bar> range from -7 to -9% of the two-body terms for equilateral triangular arrays and from 35% to 47% of the two-body terms for linear, centrosymmetric systems.