We investigate the optical response induced by a dc current flowing in a nonmagnetic material that lacks inversion symmetry. In this class of materials, the flowing current experiences a nonlinear Hall effect and induces a nonequilibrium orbital magnetization, even in the absence of spin-orbit coupling. As a result, an orbital-driven Kerr effect arises that can be used to probe not only the orbital magnetization but also the nonlinear Hall effect. In addition, in the long wavelength limit, the nonlinear Hall effect leads to a rectified current that can be used to detect terahertz radiations. We apply the theory to selected model systems, such as WTe2 bilayer and metallic superlattices. The nonequilibrium orbital Kerr efficiencies obtained in these systems are comparable to the largest values reported experimentally in GaAs and MoS2, exceeding the values reported in metals and suggesting a large terahertz current responsivity.