I know Disney owns the ones from The Muppet Show, and Sesame Workshop owns the Sesame Street ones, but where do the ones from other works fit in? Who owns the SNL Muppets, Dog City, etc?

I think the Henson family has the legal rights to those, but I'm not sure.

Disney owns all the non-Sesame Street Muppets. They were all part of the sale of Jim Henson Productions.