This subject is hard because there is no way to actually spell out these sayings. Army is like Hoo-ahh, but they say it really fast, so it just sounds like h-ugh. Navy is Hoo-yah. Now Marines is traditionally Ooo-Rah, but I have heard it different ways to include Hoo-rah and Err-ah. I believe this theory, as it makes the most sense.
http://www.angelfire.com/ca/dickg/oohrah.html