I just realized you were talking about live voice chat, not assynchronous. I guess I should have slowed down and read more carefully.
I don't know what your meeting size or budget is, but I use Elluminate as our live classroom meeting space. It has full-duplex audio with some solid audio controls as well. You can turn individual mics off and on or have up to 6 speaking at the same time and there is a hand raise system. Believe me, moderating tools in a voice discussion is helpful. Without a way for students to get signals for turn-taking everyone spends way too much time apologizing for speaking at the same time.
Another consideration for audio is to encourage everyone to use a mic with headset, not open speakers. I still have a few students with open speakers and it is very distracting to hear your own voice echo back over the mic as you are interacting. Open speakers also multiply voices when you have activities where everyone is answering in audio at the same time. Instead of 6 voices it can sound like twelve if there isn't a push to have the students use headsets.
Another thing that I like about Elluminate is that you can help the student with volume settings on their mics on-the-fly as the lesson is in progress. If they are suddenly very loud, Elluminate itself will turn down the mic. You have a + and - button to make adjustments on anyone's mic as they are speaking. Everyone has their own controls as well so that they can make adjustments. There is a gauge that shows transmission strength.
You can get a free 3-seater Elluminate room, called a vRoom. You can get a 10-seater for as little as $50/month. For about $320 per month you get more tools and you can record classes and store the files on Elluminate servers for interactive playback. This is more than a movie of what happened in the class. The students that watch a playback can interact with material, recieve files, and more. The free vRoom is good for testing it out and you can try it out working directly with a student or two that needs help. You can sign up for a vRoom at this link: http://www.elluminate.com/vroom/
I have focused on audio, but it also has a great whiteboard system as well. I can give you training for free if you want. Just contact me and I will send you a link to my classroom for a tour of the tools.
Can it integrate into a webpage? Yes and no. You can post a link that will take them into the classroom. Does it take place on your page itself, no.