I wouldn't use hot glue. The result will likely look like an elephant booger with a volume knob. I suppose you could get something more attractively organic if you had sculpting skills. Even then, the surface will get chipped up and dirtied easily.
Search the electronic part distributor catalogs, and your local stores. You might find the perfect enclosure.
If you really want to encase this thing in something permanently, the easiest thing to use would be potting compound, available from any big electronics distributor. It's made for environmental sealing of electronics from weather and chemicals, or when black instead of transparent, for security when someone doesn't want the parts used to be visible.
If you aren't going to subject it to big temperature swings, you could use one of the hard types, pot it using a too-big box as a mold, then cut away the mold and excess potting compound with a band saw or jig saw, giving nice clean edges. Then you can shape and smooth it with sand paper. This would work best if the jacks and volume knob are all on the same surface, so that can just be oriented upward, with that surface being set by the level where you stopped pouring the potting compound.
The only problem with potting compound is that it's somewhat expensive. The smallest container Digi-Key carries is 50 mL for $14. That's the price of a good case. Your board looks like you could get away with as little as about 30 mL if you're making a rectangular solid shape, so this isn't terribly wasteful.
