I'm looking for a mod that will stack multiple smaller souls to fill a larger soul gem. Is this possible on 360?
No. There are no Xbox mods for Skyrim (and there probably won't ever be either).
If you have a modded 360 you can install mods. When you extract the files from the DVD the folder structure is the same as the PC version, and you can install mods the same way. Some mods don't work correctly, but most work pretty well. This may be illegal in most countries because you must bypass DRM/copy protection mechanisms in the xbox. It might be legal if you own the game (because you wouldn't have modded your xbox with the intent to pirate games), but I'm not a lawyer.