Cluin has the explanation for bodhrans. Why anyone should make similar fun about banjos has always puzzled me. Perhaps it's because they look like bodhrans with strings? I think it's much more an 5-string American joke - people don't seem to make jokes about tenor banjos in Irish music. Not twice anyway.

Actrually the instruments that gets most groans (other than the newly bought bodhran with a bodhran basher to match) are the supernumerary guitars. One guitar, good, two ok. Three just about possible, but...Four or five and it's a din.

But then that goes for just about any instrument, except fiddles.