Minwax makes a combination one step stain and varnish. Forget the name (Polyshades?) but it's commonly available. Trick will be keeping it away from that ribbon element! Do the oak panels come off?
Otherwise, use a stain followed by varnish of the appropriate gloss.
I'd give them a light sanding with fine sandpaper (around 220 grit), tack the dust off with a tackcloth, and finish. Protect the tweeter with tape if you can't remove the wood.
I've only seen pictures of them in audio mag back issues. Very handsome. Do they sound as good as they look?