Well, loony. This is rather ironic. Your game is glitched so bad, that the seemingly only way to bypass this glitch short of sending your disc to Bethesda, is to mod.
So, me being the good person I am and as a representative of the modding community, I'll make you an offer.
Send me your save file, and I will mod your character for you in any way you like. Any level, any amount of XP, any SPECIAL, any skill levels, anything. Just tell me what you want. This should, in theory, bypass the glitch. And if it doesn't get rid of the glitch, then I can just give you whatev level you want.
Here's what you need to do:
1/ Go to your Fallout save on your Xbox, the one you want modded, move the save onto a USB.
2/Put USB into comp, put the file onto your desktop through normal windows interface if you can. If not, use a program called usbxplorer, or usbxtaf, try the first one first. Google em.
3/Upload the file to mediafire
4/I'll mod it, give you a download link, you'll download it
5/Put the file back on your USB
6/Move it back onto your console's HD.
Anyone who thinks modding is all bad is an idiot. ;)
Nazi Mod Ever <3