Anmish lets you choose a caricature of a world leader and then lets you put words in his/her mouth for thirty seconds via a microphone. While you’re recording, you can also easily change facial expressions on your caricature by pressing a letter on your keyboard. It doesn’t appear you can embed the video, though you can share a link to it. You also have access to parodies created by other users, which might make it problematic for classroom use.
Nevertheless, I’m adding it to The Best Sites To Practice Speaking English.