Employing a modified Z-scan technique at 2 K, we monitor not only the fundamental (omega) but also the frequency-doubled (2 omega) and tripled (3 omega) Z-scan responses in Cu2O when the input laser frequency omega is tuned to the two-photon quadrupole polariton resonance. The Z-scan response at omega allows us to accurately estimate the absolute number of polaritons generated via two-photon absorption. A striking dip is observed near the 2 omega Z-scan focus which basically arises from Auger-type recombination of polaritons. Under high excitation levels, the (3 omega) Z-scan shows strong third harmonic generation. Based on the nonlinear optical parameters determined, we estimate the experimental polariton density achievable and propose a direction for polariton-based Bose-Einstein condensation in Cu2O.