We investigate experimentally multi-orbital effects in high-order harmonic generation (HHG) from aligned CO2 and N2O molecules by intense femtosecond laser fields with linear and elliptical polarizations. For either of the aligned molecules, a minimum in the harmonic spectrum is observed, the position of which shifts to lower-order harmonics when decreasing the intensity or increasing the ellipticity of the driving laser. This indicates that the minimum originates from the dynamic interference of different channels, of which the tunneling ionization and recombination are contributed via different molecular orbitals. The results show that both the highest occupied molecular orbital (HOMO) and low-lying HOMO-2 in CO2 (or HOMO-1 in N2O) contribute to the molecular HHG in both linearly and elliptically polarized strong laser fields. Our study would pave a way for understanding multi-electron dynamics from polyatomic molecules irradiated by strong laser fields.