Wade, since the walls are darker than under the pictures, it is possibly just dirt on the walls. If the wood appears to be reasonably well finished, try washing with Dirtex and try to use as little Dirtex water and rinse water as possible but enough to do the job.
Is it possible that smoke from a fireplace or cigarettes caused this? That's pretty common. If the Dirtex doesn't work, then a solvent might be appropriate. I have some stuff in the works that will save me answering the same question over and over but it's not posted yet. E-mail me if the Dirtex doesn't help.