While I don't use the Xbox system for NV, have you tried going to Settings/Controls/Default? And in fact setting default to all the Settings and see what happens. Other than that, I'd guess deleting your Options Save file, that is not your game file, and creating a new Options file via a new game and then going back to loading your old game. I'll explain:
- Set all your Settings to default and see if this works.
- Copy your options file, just in case, to a physical media, and then delete it from your system.
- Exit the game, restart it and begin a new game.
- Save a new option file, this should happen automatically if the game discovers you don't have one.
- Load your original game file.
I should point out this is merely advice and I haven't experienced this, I'm just attempting to help.
Reno