This is exactly the question I was coming here to ask. The wallpaper is completely down, but the walls are shiny and sticky to the touch. We've tried soap & water, vinegar & water, DIF, Goo Gone, Goof Off, TSP and sanding - NOTHING has worked. Desperately need help!

I would then try DIF and an abrasive pad to remove the adhesive. I will take a bit of elbow grease as some of these adhesives can be difficult to remove, but you don't want to paint over adhesive.

Well, I talked to some people at Hirshfields today and they said it sounds like what's on the walls still is sizing, not adhesive. They said to just prime first with a good oil-based primer and I should be fine...