I'm trying to create a new league (Alpha Ethniki) And add all the Greek teams into it such as: Olympiakos, PAOK, AEK, Panathinaikos etc. (I downloaded a patch for more Greek teams) However, all the teams are in the rest of the world category, and I want to transfer those teams into my new league.

Anybody know how to do this?

And also, can I use this league in career mode, if so how do you put the league into a region?

You can't do that with the CC. Use Tournament Master.

to change the league that the teams are in, you must use dbmaster, and change them yourself... I don't know of any way to do it using CC.

As far as career mode goes... you have to use tournament master and setup the league yourself.