Hi there, I'm visiting in Massachusetts and just borrowed a machine to check in with the Mudcat folks. Yes, I yodel, or at least am well on my way to learning, and I have had classical voice training (way back when I was a sprout). I also know of a "Learn to Yodel" kit that a singer out in the West (Colorado, I think) named Liz Masterson has. When I get back to Wyoming, I can find her address if anyone's interested.
I CAN say that if you were serious about getting a sore throat from your attempts, Fair Youngmaid, you probably are straining at it. A light touch is better than working at it hard, and part of the trick is figuring out the melody of the passage you're wanting to yodel and, believe it or not, the "words." It matters if you say "oh-di-lay-ti-yicky-oh," or "ah-di-lay-ti-i-ho..." (WHATEVER), so slow it way down, get the tune sorted out, practice it slowly and with the same syllables, just as you would with any other song you're learning, then speed 'er up.
Worry less about getting the "break" in your voice at first than just learning the melody of it. Then you'll be able to work at the fluidity later.
Also, if you want to sing clearer and better on your pitch (in either yodeling or just plain vanilla singing) visualize yourself coming in from on top and landing on the pitch or note, rather than trying to reach up to it. That will give your voice more buoyancy and cause less strain (and less flatness...)
Hasta later -- y buena suerte, KC