I couldn't find anything online so Im asking here....

1. Do you need a permit to hunt these ?
2. What caliber would be best to take these down? I have a .270 but probably not going to do it, right ?

thanks for the help!

1. They're an exotic, so I'm not sure, but I think the state wants you to have one, even though there's no tags/tagging, etc.
2. I've never hunted them, but I have hunted a lot of other stuff, and I'd bet your .270 is just about perfect. (Unless you're just looking to buy another gun and then it's completely inadequate. )
3.

Yes, you need a license to hunt exotics in TX. If you are a resident, then all you need is the general hunting license. If you are a non-resident, you can get a non-resident hunting license or a 5-day exotic hunting license (which is much cheaper).

Your .270 will be fine as long as the load you are using has a sufficiently sturdy bullet. Aoudad tend to be tough, and can be in some pretty rugged country (depending on where you are hunting them), so a bullet that can punch through both shoulders is best.

.270 is plenty. My 14yr old killed one with his .243. It ran about 20yds and face planted.

Nosler AccuBond or Hornady GMX will do well

shot placement will do it. congrats