When ordinary cleaners don't work, stubborn stains on plaster often can be scrubbed away with a strong solution of tri-sodium phosphate (TSP) and water or a non-phosphate substitute.

Unpainted plaster is porous but generally non-soluble, so unless you really drown the wall it can take a good bath and rinse.

Drywall has a paper coating and its gypsum base is water soluble, so water can penetrate a thin coat of paint. Scrub drywall gently with a soft sponge and a mild TSP solution, and try not to use too much water. Let the drywall dry thoroughly and consider repainting with a higher-gloss paint that resists stains and is easier to clean.