We report numerical results on the velocity statistics of topological defects during the dynamics of phase ordering and nonrelaxational evolution assisted by an external shear flow. We propose a numerically efficient tracking method for finding the position and velocity of defects and apply it to vortices in a uniform field and dislocations in anisotropic stripe patterns. During relaxational dynamics, the distribution function of the velocity fluctuations is characterized by a dynamical scaling with a scaling function that has a robust algebraic tail with an inverse cube power law. This is characteristic of defects of codimension 2, e.g., point defects in two dimensions and filaments in three dimensions, regardless of whether the motion is isotropic (as for vortices) or highly anisotropic (as for dislocations). However, the anisotropic dislocation motion leads to anisotropic statistical properties when the interaction between defects and their motion is influenced by the presence of an external shear flow transverse to the stripe orientation.