The photo-induced enhancement of second harmonic generation and the effect of nanocrystal shape and pump intensity on confined acoustic phonons in semiconductor nanocrystals have been investigated with time-resolved scattering and absorption measurements. The second harmonic signal showed a sublinear increase of the second-order susceptibility with respect to the pump pulse energy, indicating a reduction of the effective one-electron second-order nonlinearity with increasing electron-hole density in the nanocrystals. The coherent acoustic phonons in spherical and rod-shaped semiconductor nanocrystals were detected in a time-resolved absorption measurement. Both nanocrystal morphologies exhibited oscillatory modulation of the absorption cross section, the frequency of which corresponded to their coherent radial breathing modes. The amplitude of the oscillation also increased with the level of photoexcitation, suggesting an increase in the amplitude of the lattice displacement as well.