Odette has two voices: Liz Callaway (who sings in The Swan Princess), and Michelle Nicastro (who speaks in all three movies and sings in the two sequels). Both are stage performers with beautiful singing voices though sadly I have not seen either perform live. Here I'd just like to mention a few other places I've heard them sing.

There was a little fantasy tv series a while back called Xena: Warrior Princess. It was cheesy, it was fun, and it had a warrior princess who dressed in leather and roamed the countryside generally trying to save people and stuff. One of the most surreal episodes they had was a musical episode called The Bitter Suite. In it, everyone sings because... well... It'll take too long to explain, so suffice to say that everyone sings.
One of the characters is a blonde warrior princess-wannabe called Callisto, played by Hudson Leick. She too, starts singing in that episode, and when I first heard her I thought, hmm that sounds oddly familiar... I got the episode soundtrack quite some time later and to my surprise, found that Callisto's singing voice was none other that Michelle Nicastro.
Ms Nicastro's singing voice in The Bitter Suite is quite different from the voice we hear in the Swan Princess trilogy. She manages to hit harsher almost rock-like notes at times, though the general honey-sweetness is still there.
Duration: 11 secs, Size: 178 kb
As an addendum, Michelle sadly passed away in 2010, RIP.

Ms Callaway's singing voice has been used for quite a number of animated heroines other than Odette. Those I know of are: