“My neighbor has 2 large dead oak trees leaning toward my property, with the possibility that at any time they could fall causing damage to my home and/or cars. Since he has made very little effort to correct this situation, except to attempt to pull them down a branch at a time using his fishing pole and a rope. Can he be held responsible for damages?”
The short answer is yes.
Dead trees, or even live trees, that present a real danger of falling and injuring people or damaging structures are considered a nuisance, and can be required to be removed. You probably don’t want to go through the trouble and expense of a lawsuit (not to mention how it would affect your relations with your neighbor), but your city and/or county may have a mechanism in place to deal with dead and dangerous trees. Try calling around.
Keep in mind, however, that your say-so may not be enough to get the tree removed. In most cases where the law gets involved, you’ll need the opinion of an expert–in this case, an arborist–to confirm that the tree is dead and is a real danger. This alone can be pretty expensive.
One thing you might want to consider: Your neighbor probably doesn’t want to spend the money it’ll cost to have the tree professionally removed. If the tree does fall and do damage, his homeowner’s insurance will be on the hook for it. A word in his ear about what that’ll do to his premiums may help change his mind.