Dissipation caused by Gravitational Wave Emission Two massive bodies orbiting each other can lose energy through gravitational wave emission until colliding.
Can a single massive body, moving with constant velocity with respect to an observer, lose it's kinetic energy to gravitational waves? I get that changing the position like this without oscillating doesn't result in a wave exactly, but mustn't the new information about the gravitational field still be transmitted, resulting in energy loss?
 A: The answer and reasoning for this are exactly the same as in electromagnetism. (Assuming the observer is far enough away and has light enough mass that we can ignore the effect the observer has on spacetime for the massive body).
Since the massive body is traveling at a constant velocity (below $c$), we can go into its rest frame. Since it obviously isn't emitting waves in its rest frame, and since the laws of physics are the same in any inertial frame, it is also not emitting waves in the observer's rest frame.
At this point I am going to transition to talking about electromagnetism, because the correct words are probably more familiar. But, the logic here can also be transferred to gravity (to leading order in perturbation theory). The electric field due to the "static" part of the field (not the wave) falls off as $1/r^2$, where $r$ is the distance to the "charged body" (assuming, since we've moved to electromagnetism, that the body has a net charge). The electric field due to an electromagnetic wave sourced by an accelerating charged body falls off as $1/r$. If the charged body is moving at a constant velocity $v$, the information about the changing $1/r^2$ part of the field, does indeed travel at $v$. You can imagine that in some sense, the entire $1/r^2$ field configuration is moving at a constant velocity. If the charge accelerates, this information needs to propagate to the observer somehow, which it does in the form of a wave.

The above image, from the textbook by Purcell and Morin (which I grabbed from this website)
shows how an electromagnetic wave communicating the change of a particle's velocity to a distant observer. Far away (far enough that light has not had time to propagate since the particle accelerated), the field lines move at a constant velocity, and point to where the particle would be if it hadn't accelerated.  Nearby, the field lines point to the current location of the particle. In between the near and far regions, there is a visible shell, which is the wave (remember that the electric field points perpendicular to the direction of propagation of a wave). The wave communicates to the distant observer, that the point charge has accelerated.
In gravity, at asymptotically large distances away from the massive body, the spacetime curvature falls off as $1/r$ for gravitational waves emitted from the body (if its quadrupole moment changes with time), and $1/r^2$ for a body that is static or moving with a constant velocity. We can make the same conceptual split; gravitational waves carry information that tell a distant observer when the quadrupole moment of the mass distribution of the source changes, much like electromagnetic waves carry information that the dipole moment of the charge distribution changes. A massive body moving at a constant velocity does not lead to gravitational waves. This description and connection to electromagnetism relies on perturbation theory; there are also more rigorous descriptions in terms of quantities describing the asymptotic behavior of the spacetime like the Bondi news, but this does not change the answer to your question.
