Nowadays, Oak and Leather cases are more for looks than for travel. They should include an assortment of turn screws that are sized to fit the gun. They should contain a bottle of oil and maybe some lube or even vaseline. A couple of snap caps, maybe a pouch with some cleaning accessories. The cleaning rods would be stored under the barrels.

I would guess whether or not you can carry ammunition in a case with the firearm would depend on where you were. In the US you can travel with both if the ammo is in an protective case.