I pulled down the 1960ish paneling to check for mold after all these years. Fortunately, there was only a small area that had mold and it can easily be replaced. Unfortunately, each panel had a line of glue along with the nails.

Anyone have any suggestion on how to remove very strong glue. One suggestion was to sand it-I tried, I don't know what type of adhesive they used, but I sanded for hours and it didn't make much of a difference.

I am trying to avoid sheetrocking the entire room again just to get rid of glue lines.

The best may be to scrape the glue lines off which will take some the paper from the sheet rock. And with a little skim coating you can make it smooth. But at least you won't have to tear everything out.
-Dan

I don't have any advice about taking off the glue, but you might try this website http://painterforum.com/ It's a forum for professional painters and has a section where they answer home owners' questions.

Belt sander. But the adhesive will probably clog up the sandpaper so make sure you have enough. It will also tear up the sheetrock so you will have to skimcoat it afterwards. Also use a stain blocking primer to prevent any residue leaching through the paint. I have the same problem in my 70's addition in my house. But they just put the panneling up on the studs. I did not want to rip out the panneling for just this reason. Sheetrocking the entire room right over the panneling.