We show that a combination of a fundamental pulse with linear polarization along the vertical direction and an elliptically polarized second harmonic pulse with both vertical and horizontal electric field components can be used to orient linear molecules efficiently, leading to higher degrees of orientation. Due to this specific combination of polarizations, the asymmetric hyperpolarizability interaction potential, which remains the same as that in a linearly polarized two-color laser field, is created along the vertical component of the elliptically polarized second harmonic pulse. On the other hand, the horizontal component suppresses the otherwise strong symmetric polarizability potential responsible for alignment, increasing the tunneling probability from the shallower potential well to the deeper one. As a result, the degree of orientation increases and can be controlled by changing the intensity of the horizontal component of the elliptically polarized second harmonic pulse. This study is the generalization of the all-optical molecular orientation technique based on the anisotropic hyperpolarizability interaction.