You cannot. You can go even less online than with the PS3. With the xbox, you are sure to get hammerbanned with the banhammer as sure as you go online.
There is ONE exception to the rule. If you got a demon installed in your Xbox. A demon is basically a dual NAND solution, where you can swap between booting on CFW(or whatever you want to call your freeboot image or similar) and OFW.
You would most likely know, if your Xbox had demon installed into it, its quite expensive