A theoretical and experimental study is made into the combined manifestation of local and nonlocal optical responses in a cubic nonlinear isotropic medium such as an aggregated colloidal silver solution. The phenomenological treatment of polarization effects is performed for the general case with due regard for the frequency dispersion of both local and nonlocal nonlinearities and for the noncollinear propagation of pump and probe light waves. The inverse Faraday effect, the optical Kerr effect, and the self-rotation of the polarization ellipse in a fractal-disordered nonlinear medium are observed for the first time. The tensor components of the local and nonlocal cubic nonlinearities of colloidal silver solutions are measured for different degrees of aggregation. It is demonstrated that, as the size of silver aggregate increases, the nonlocal nonlinear response increases much more strongly than the local one. An inference is made that the mechanical motion of metal nanoparticles because of their dynamic interaction with the light wave field can contribute to the nonlinear polarization effects.