Electrokinetic phenomena in a nematic fluid are considered, involving either fluid flow under designed director patterns, or particle motion when one or more dielectric particles are suspended in the nematic matrix. The long range orientational order of the nematic constitutes a fluid with anisotropic properties that enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. We present a quantitative transport model of the mechanisms inducing spatial charge separation in the nematic, and of the structure and magnitude of the resulting flows. The fundamental solutions for charge distribution and flow velocities induced by designed periodic director patterns, and by isolated disclinations are given. The same model is used to study the motion of a single particle-hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.