Under the Neil sculpture is a wooden base with heavy wood dowel supports. The rest of the sculpture is a mix of paper mache, small figures with wire armature, even smaller figures (like the tiny puppets, which are resin) and leather. Thick paper mache is very, very strong, and when treated properly, can last ages. When I make a larger sculpture, I have to have a fair idea of the finished piece to make a good choice for armature. Depending on the type of piece, balance and weight distribution, I will use wood, steel pipe or pvc, or a mixture of the three.
The mechanics (I plan to post a short movie) are accomplished with motors and cams that create very simple up and down movements for the arms and back and forth for the heads. The secret to those is lots and lots of trial and error, quite a bit of cursing, and years of taking toys apart and looking inside.
Thanks for the question!