I have serveral older houses (nice rental houses). Painting over wall paper is not ideal --- or advisable. If you have a wall were there is wallpaper (the whole wall or small sections of the wall), applying a water-based paint (e.g., latex paint) can act much like the process one might use to remove the wall paper. That is, you soak the wall paper with water then you easily scape it off the wall. With a water based paint, you are soaking the wallpaper (to some extent--depends if moisture in paint gets down to wallpaper layer)--- and not scaping. Hence, the wallpaper's adhesion to the wall is weaken-- it may or may not peel off. --- Or, as possible in your case, only sections of the paper may peel off. You state, that walls in this area of the house have been painted 3 times--- it is very possible, that each time it has been pained, different sections of wallpaper have loosened enough to come off---- Hence, the good news is (if wall paper is the problem)--- it will take only 3 or 4 more paint jobs to get off all the wallpaper! I have painted over wall paper, with a waterbased paint--- it CAN be done; however, one must qucikly coat an area with paint--- if you linger over an area on the wall you are asking for trouble--- get a coat on an area and move on! ---In other words, if you fill your roller, and try to "streach" the paint--e.g., try to cover a 5 ft sq. area of wall with one roller full of paint you are over staying you welcome in that area of the wall and you are begining to weaken wallpaper bond. Three things to try in order of easiness: (1) paint as instructed above, (2) pick one wall of a room in question (a wall that has been most problematic (and soak a cloth with water--- wet down a section of wall (e.g., a 5 X 5' section)--- do as you might for removing wall paper (several repeated soakings--- ask a wallpaper store about how if necessary)--see what happens---does paint & wallpaper peel off? If so, you need to do whole wall. (3) You CAN hang drywall over existing wall; however, existing moulding and baseboards with have to be dealth with --might not be correct lenghts after a layer of drywall is applied over existing wall. And it is expensive--someone might even suggest that you remove the lath & plaster then drywall -- Unless you have unlimmited money and unlimited tolerance for mess-- I would not consider this option. If I were you I would try options (1) or (2)--- if wall paper is problem--- get a wallpaper person to see if they will strip off a problemed wall (this will be a test of their skills (don't give them the job of stripping the whole downstairs-- test their skills/solution to your problem on one wall. Good luck. Jaes.