In this study, we investigate Einstein-Aether (AE) theories of gravity using the post-Minkowskian approach. These theories extend the spacetime metric by adding a dynamical, long-range vector field with a fixed norm. We focus on a three-parameter subclass of AE theories in which the speed of tensor gravitational waves is the same as the speed of light, a fact established to extraordinary precision by the observation of gravitational waves and gamma ray bursts from the neutron star inspiral event GW 170817. We apply the formalism of post-Minkowskian theory and the Direct Integration of the Relaxed Einstein Equations (DIRE) to AE gravity, with the goal of deriving equations of motion and gravitational waveforms for compact binary systems to high orders in a post-Newtonian expansion. Our analysis incorporates Eardley's method to parameterize how variations in the aether field affect the mass of self-gravitating bodies. This approach sets the stage for future high-order calculations and lays the foundation for testing gravitational Lorentz invariance through precise observations of compact binaries, potentially revealing new insights into deviations from general relativity in strong-field regimes.