We present a novel method for extracting the hydrodynamic and electrostatic interactions of anisotropic colloidal particles. By measuring the correlated diffusion and drift of interacting clusters of particles, we can experimentally measure the mobility tensor and forces/torques on each particle. We apply this method to measure the electrostatic interactions of anisotropic particles in the limit where screening length is much larger than the particle size---relevant to microparticles in nonpolar solvents and nano/bio colloids in water. We find dramatic departures from the predictions of Debye-Huckel theory.