There are clubs and organizations in medical school? Or is that fancy speak for bars? :-D And bars may be the best place to learn public oration.
Though in all seriousness, you will get used to public speaking VERY quickly in medical school, when you have to present patients and cases. The good news is that a lot of it are formatted that you know exactly the way you instructors, attendings/etc will want them (after they yell at you).
Wait until you get into residency and have to do M&Ms. That's like public speaking and public crucifixion all at once!