The light polarization dependence of two-photon absorption (TPA) near half the band gap has been experimentally investigated in strained-layer multi-quantum wells. A detailed analysis of their TPA photoluminescence spectra, measured for two different polarization configurations of the exciting laser beam (perpendicular and parallel to the QW growth axis z), permitted us to sensitively probe the exciton anisotropy in quasi-bidimensional (Q2D) heterostructures. Fundamental and excited exciton states of different symmetry have been selectively detected by exploiting the strong anisotropic selection rules for TPA processes. In particular, the polarization along the z axis allowed us to obtain the first clear experimental evidence of higher-order light-hole excitons. Our experimental results are in good agreement with theoretical predictions of an analytical model of TPA in Q2D exciton systems, demonstrating the usefulness of a simplified approach for the case of photon energies close to half the band gap.