live trap and take them to the nearest animal control center (or return them to the neighbor if safe to do so). Document every time you do it. Talk to local law enforcement to get their advice and opinions (so that is the neighbor gets unhinged you have law enforcement on your side).
killing the cats is probably a bit of an extreme first step.
People who 'love' their pets should be willing to take responsibility for them. If they are not to allow the pets off their property and the cats are getting off of the property then they aren't being responsible. Period.