We have had similar problems. When an association member caused road damage through ATV use, he was billed for the damage, and that pretty much took care of that problem. As for use by outsiders, we found which property was being accessed and used by the ATV's. It was a wood lot, and the owner wasn't aware of what was going on. When we notified him, he willingly posted his property "no ATV's," and once word got around, use of the road by ATV's pretty much stopped. If that hadn't worked, the next step would have been to get a forest warden to post trail cameras to catch who was causing damage to forest land in production, which is a class E crime. But that's only an option if there is damage to forest land or farm land in production, under Title 17, section 3853-D. (It also applies to "public easements," but most road association roads are private.)
Another avenue, since you say at least part of the problem is underage drivers of ATV's, is to try to find the parents of the underage drivers and inform them of what is going on. (This may require following the tracks, or actually following the ATV's home.) If the parents find out their kids are going where they don't belong and causing damage which the parents may have to pay for, or that their kids are speeding, that may end the problem. If it helps, you can tell them that you know of at least one road association where a non-member on an ATV took a corner too fast, skidded on the loose gravel, and crashed into a rock off the side of the road. He was taken away by life flight. (We never did hear the outcome.) No one wants to see that happen again.