If your cases are just a little dusty, you can vacuum them out with a brush attatchment or just dump them over on some grass a few times. Dirtier, see below.
To clean cases with type in them, you can take a piece of window screen (fine mesh) and secure it over the top of the vacuum cleaner wand (take off the attatchments and rubber band it right over the end) and then vacuum out the dust and dirt. This way the type won’t get sucked up. Or, if you’re really bored, take out all the type and set it up in a galley, tie it up securely, and brush the top with a soft type brush. If it’s really gunky you could hit it with a damp cloth with typewash. I know someone who has cleaned all of his type in lye, but I try to stay away from it. If the type is just dusty brushing it will take care of it.
I’ve even gone as far to take out the type, rip the bottoms off the cases where the old plywood was delaminating, cut new boards from Luan plywood and nail them on, then spray the whole case with a clear polyurethane. For smelly cases, pick a really hot day, spray them with vinegar and then let them dry in the sun. Kills the musty smell, mostly. I’ve squirted really gross cases out with the hose, quickly, and let them dry in the sun with no problems, too (but not if they have that chipboard bottom, that will deteriorate.)
I have cleaned way too many cases and am currently about halfway though a wooden 2/3 cabinet- tying the type, sanding the fronts of the cases, cleaning out dust and dirt, and then staining the front/polyurethane on everything else. The cabinet looks great now- a fine piece of furniture!
Don’t forget to wear a mask when you’re vacuuming/sanding/making lots of dust, especially if there were mice in the cases.