You can start with Effects> Distort> Mesh Warp. You'll likely need to isolate sections of your image with a mask and make duplicates of the footage with varying masks to control how the warp affects given individuals.
The puppeteer tool will also do some of this effect, and is a bit more free-form interactive. You just place pins on the "pivot points" you want to manipulate and then move them over time. You can adjust the motion paths for each pin so there's a great deal of fine tuning possible, and you don't have to do as much masking.
Digieffects makes Freeform AE which is designed to do exactly this sort of thing. I have not had much chance to work with the demo version, but if it's in line with their other plug-ins, I'd say it will have some very nice features. I think it's in the $99-$199 range, but you can try the demo first.