"å vaske opp" means "to do the dishes" or "to wash up". "clean up" would be "rense opp", "rydde unna", "gjøre rent (i)". "vaske opp" has a very unambiguous meaning in Norwegian, and is not confused with other kinds of cleaning. "vaske" on its own, on the other hand, would be "wash" or "clean". I hope this made sense!
This comment is 6 months old already but since you never got an answer I figured I'd chime in haha. I'm American and for me, "washing up" makes me think of washing myself up, usually my face or hands. I'm specifically from New York, so I'm not sure if other parts of the country use "washing up" to refer to dishes or not.
Examples like this always get my Norwegian partner angry - she says that elsker just isn't ever used apart from when the "love is a deep, truly meaningful passionate affection, the kind reserved for married couples and Romeo and Juliet!" And that this particular example would mean that the son in question has some deeply troubling feelings towards dishes!