Erm... sorry? The Toribash directory is the Toribash folder. Please explain more clearly.
If you’re looking for the folder in itself, then it’ll be under Program Files, then Toribash 3.05, 3.06, etc. (on Windows), or simply the Hard Drive area on a Mac.
If you're looking for a way to run the executable outside of the Toribash folder, you'll have to copy the whole lot, including the data folder and sub-folders (obviously).
I'm not sure how any of this can help you run a mod online. Keep in mind that you can't create new servers at the moment (not until the new ToriLauncher is released), so unless you have the privilages to modify an existing server, you won't be able to pull it off. (correct and smite if I'm wrong, mods)