How do you remove adhesive used to put paneling over congoleum on a basement wall?

I think the best way to do this would be to employ a sand blaster. It's no doubt messy but with care will be the quickest way to remove the adhesive. There will be massive damage to the congoleum (why is this on the wall and not the floor). Consider removing the congoleum with the offending adhesive and then going forward with your redesign. Perhaps when all is said and done you might just wish to fix new drywall to the congoleum using some 2x4 or 2x2 . This would allow you to add increased insulation behind your handywork. Never a bad idea in a below ground basement.