Here, we demonstrate how the light-induced birefringence due to the dipole molecular realignment and anisotropic polarizability of a nematic liquid crystal inside a droplet changes the droplet's radial (and thus optically isotropic) structure into a birefringent one. This intensity-dependent change of birefringence can be understood in terms of the anisotropic polarizability and orientational optical nonlinear effect. Birefringence induced by laser tweezers changes the momentum of the passing light. In turn, for the circularly polarized tweezers, this change generates an angular momentum change large enough to spin micrometer-sized droplets. For the linearly polarized tweezers, the molecular ordering generates momentum, which laterally displaces the droplet. It is shown that the optical nonlinearity can be 'large' enough to have mechanical (ponderomotive) implications, that is, it allows control of the movement and position of micro-objects with submicrometer resolution. The optically induced molecular alignment controlled by the polarization and power of the laser tweezers allows one to actuate, rotate, and translate objects which are up to 10(3)-10(4) times larger than the constituent molecules themselves.