The bodies are silicone and the heads are a hard material, probably cast from resin.I can't tell if the mouths are clay or replacements made also of a hard material. The seams could be blended out either using same-colored clay or digitally. To be honest though, it almost seems like they're using full replacement heads, at least sometimes. I never see a flicker of colors or textures changing though, so I'm not sure.
I suspect full replacement heads at least sometimes. If you notice. the expressions don't usually change except during a cut. There's one expression for a full shot, then next shot there's a different one and it holds until the next cut. This seems to hold true until there's dialogue.
Of course when the guy's head morphs that's done with clay and some hair, and the eyes are a hard material.