Refraction at a dielectric interface can take an anomalous character in anisotropic crystals, when light is negatively refracted with incident and refracted beams emerging on the same side of the interface normal. In soft matter subject to reorientation, such as nematic liquid crystals, the nonlinear interaction with light allows tuning of the optical properties. We demonstrate that in such material a beam of light can experience either positive or negative refraction depending on input power, as it can alter the spatial distribution of the optic axis and, in turn, the direction of the energy flow when traveling across an interface. Moreover, the nonlinear optical response yields beam self-focusing and spatial localization into a self-confined solitary wave through the formation of a graded-index waveguide, linking the refractive transition to power-driven readdressing of copolarized guided-wave signals, with a number of output ports not limited by diffraction.