Try this: I forget what mission it is but it involves collecting debts for the Atomic Wrangler. One of the guys is located on the Strip and you are told to "kill" (don't have to) him. Whatever you choose, make sure to take his hat. His hat is the key to getting on the Strip. Simply wear his hat when entering the Strip and it should work. I do not know why it works (saved data mumbo jumbo) but my friend tried this same technique and it worked. However, whenever he tries to manually save his game on the Strip it freezes. Basically, I would just use this technique until a patch comes out that fixes this bug. Hope this helps. Feel free to contact me if you're confused.
If you already gave the hat to the woman at the atomic wrangler, then you can buy a "old cowboy hat" from the vender in the crimson caravan HQ. You should be able to get into the strip and autosaves wont freeze it up. I did have trouble loading a manually saved game and the autosave. Both just froze my 360 when i tried to load, but I could leave and then save and go back to the strip. I would suggest saving frequently and not always over the same save as before.