Even without an HOA, there should be a local office concerned with zoning and building codes that you can check with.

Well, I have no idea where you live but where I live if you suspect there is some damage coming from a neighbor's whatever that is built on your wall and they won't allow you to see it, I would write a letter, mail it registered, and when no response came I would ask the local authority to help. Free and then a record of the issue is filed and if a lawyer is necessary well then you've got some ammo to take to court.

You need to contact the zoning office in your town. Your current structure has probably been grandfathered into its space. There are probably lot setbacks in place now to prevent this from happening, and reworking that garage will require moving it as it wont be grandfathered anymore. You may be able to apply for a variance to change the size of the structure and keep it in the same location but further back from the lot line. I recommend at least 3 feet from the lot line for egress and maintenance on the wall. For example, zoning code in my town requires fences running parallel with the house have a 3 foot setback so both the house and the fence can be maintained and the 3 feet is the standard size of a hallway.

I'm with stolenidentity. No need to tear down and rebuild the garage until you exhaust every avenue with the neighbor. Hopefully there are ordinances prohibiting them from building on the back of your structure. Actually, since it's attached to your structure, it's yours and it's encroaching. :-) This could be used as leverage to either get them to remove it, or let you remove it. Not only that, but if 'your' structure has encroached for a long period of time and there is no written evidence which property owner built the thing or approved it, you might have a case for adverse possession of a couple feet of their property. That might light a fire under them!

Make a trip to the courthouse and look up the lot lines for your and your neighbor's property. You should be able to get plat copies (for a copy fee). You need to find out exactly where that lot line is. You may be able to get a plat showing the measurements from the building foundation walls to lot lines. If you find that the wall is a fraction of an inch over the line, you can force it to be removed.

Also, check with you town's building inspector office. There should be ordinances pertaining to drainage of adjacent properties. Usually, an adjoining property is not allowed to drain water to an adjoining property unless an agreement to the contrary has been made.

"Make a trip to the courthouse and look up the lot lines for your and your neighbor's property. You should be able to get plat copies (for a copy fee). You need to find out exactly where that lot line is."

Finding exactly where the lot line is is done by a survey which costs about $1,000.00, not a free trip to the courthouse.

Or you could buy a 'good' metal detector and try to find your property pins. Sometimes they are hard to find, or not placed, and if they are placed there may be multiple pins in one location so may not always be accurate. Plenty of possibilities but worth trying, maybe you find them easily and only one pin per corner.

I agree a judge would want a real survey done, a homeowner could have found the pins and moved them.

Another point - if the next door neighbor build on his property in a way that damages your property HE is liable for your damages. I too have a garage with a zero lot line and went through something very similar. Getting the current set back codes will have zero effect as you need the codes as to when your garage was built. If the codes have changed, you are grandfathered in.