Lungless salamanders absorb oxygen through their permeable skins. All amphibians do to some extenct. It´s not really breathing since there the lungs aren´t involved. It´s simply by diffusion. The skin is permeable and wet, and so the dissolved oxygen simply diffuses into the animal´s tissues. Lungless salamanders are able to get all the oxygen they need through their skin because they are small animals which are generally inactive and have slow methabolisms.
The flying frogs are different species that have adapted to being able to "glide" in big jumps. They have large webbed feet that they extend during a jump to encrease their surface, which allows hem to glide a little.
The most famous of these flyring frogs are probably those in the genus Racophorus.
As for other odd amphibians, you could search for info about caecilians, clawed frogs, Darwin´s frog (which carries its young inside its vocal pouch), giant salamanders ( genus Andrias)....those are all pretty interesting.