Yes, you can mod Fallout 3 and lucky it's not to complicated. Simply download Xplorer360 or (what I recommend) Xport 360. You also need to find a Fallout 3 save editor, or the G.E.C.K. modded for use on the 360. Once you have everything you need (including some sort of transfer cable, of course) you just follow the instructions, and enjoy your mods. Also there is an EXTREMELY small chance you will get caught, because if you do it right they will never be able to detect the mods.
Read for a profile tool: http://forums.techpowerup.com/showthread.php?t=77427
As for the G.E.C.K. I found a link on codejunkies.com so it will probably always be there.
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i think on xbox live you can get these thing called garden of eden pack or something it mods stuff but i don't know if you can only get it on PC
No
No it is only on Playstation 3 and not on XBOX 360. last of us is a game.
only if online
PS3 Definitely... But sometimes the XBox 360 with certain games like Halo 3