Higher-order harmonics of elastic waves have emerged as valuable for detecting nonlinearities associated with material damage, such as cracks, and those related to partial saturation with free gas. In this study, we conducted low-frequency forced oscillation measurements on Bentheimer and Berea sandstone samples under varying saturation levels, including dry, partially saturated, and fully water-saturated conditions. We also performed tests at different strain amplitudes controlling the production of higher-order harmonics. With increasing effective static stresses, cracks progressively close, resulting in a decrease in the harmonic content. At dry conditions, nonlinearities are attributed to grain contacts and microcrack deformation. Partially saturated samples exhibit nonlinearities produced by liquid bridges. In particular, the second harmonic increased for saturation levels above 79% but decreased again for nearly fully saturated samples. In contrast, the third harmonic showed no consistent trend with saturation. The theory devised by Rozhko 2021 matches the experimental observations. In particular, only the second harmonic shows an amplitude dependence on fluid saturation. We also observed a correlation between the attenuation of seismic waves and the amplitude of the second harmonic, as both depend on the saturation level. However, for the third harmonic, no correlation with attenuation exists.