I'm not entirely sure, because I don't own an Xbox 360, but I don't think it's going to happen anytime soon, if ever. Xbox 360s aren't very mod-friendly.
You'll need a PC capable of Oblivion, a PC copy of Oblivion, and a PC copy of Morrowind. Sry
The PC version of Oblivion is definitely worth the expense, though, just because there are so many high quality mods out there for free, as opposed to just the official plugins you have to pay for. I myself started on the Xbox for Morrowind, switched to the PC for the mods, and never went back.