A.H.
If you are able to draw/paint the characters, you could buy one or two (depending on the sizes needed) of those egg-carton-foam mattress things that are sold to put on your bed (not sure exactly what they're called).
Cut it into the correct shapes (rectangle and starfish), and paint the flat side to be the front. We usually use spray paint for the main color and acrylics or permanent markers for details. You can also add embellishments, such as Spongebob's tie, using cloth sewn or glued on.
We did this to make a banana costume for one of my sons last year. We just cut a hole to fit around his face: snugly so it would stay on, but not too tight. Fortunately the foam is somewhat stretchy and it's easy to cut with scissors, so it wasn't hard to get a comfortable fit. We didn't even have to secure it with anything else.
It was easy to wear, could be taken off and put back on in seconds, and was light and very flexible (no difficulty sitting down or bending over!). Not to mention, it was relatively inexpensive--and he got tons of compliments! ;-)
You could probably do the same kind of thing with large sheets of craft foam if you can find them... or you could use cardboard, although that wouldn't be as flexible and would need a way to be secured (tie-on with yarn?).
HTH! Good luck, and I hope they have fun!
--A.