Maybe the derailleur hanger is misaligned? Try standing the bike against a wall and looking at the rear derailleur cage from behind. If it doesn't look like it's parallel to the plane of the bike's frame, then either the derailleur hanger is misaligned or the derailleur's bent (or both).
In cases of a misaligned hanger, you can do a pretty good job of straightening it with an adjustable wrench to bend the hanger, then use the derailleur as a gauge (unless it's bent). There are specific tools for that, and hopefully the LBS has one if you want it done the official way.
New cables and housings might help, as you say, particularly if the old ones are corroded (Suntour cables seem prone to developing powdery white corrosion). You can slide the housings down the cables and check their condition, and perhaps oil them if they don't look too bad.