There is a misconception in your question:
it's obvious I won't be able to produce any acceleration in the car
It may be obvious to you but it isn't to me. Just because you cause a deformation does not mean that there isn't a net acceleration. Just think about a car stopped at a traffic light. A car comes up too fast from behind and hits the car in front. The bumped is bent and the car moves forward a little bit (or a lot... depending on velocities).
So even in an inelastic collision (where things deform irreversibly) you can and will transfer net momentum - there is a force $F$ applied for a time interval $\Delta t$ which results in the potential for the car to move. Of course there may be other friction in the car which results in an opposing force that stops it from moving - but there is no "law" that says there must be such a force.
In summary: inelastic impact can transfer impulse. Whether the object struck moves depends on whether there is a net force. The "equal and opposite" does not prevent a dent from happening: because there is a force from A on B, and from B on A. So the car does feel the impact, and does get dented; the wrench in return feels the force from the car.