The Other Trenchbillies only appear in the episode "Trenchbillies." They are all related somehow, and they do not like anyone to come to their part of the sea (See Ma Angler for reference).
They all look the same, just like any other trenchbilly.
After SpongeBob, and Patrick fell down a long cavern, they fell right on another trenchbilly. They were dubbed honorary trenchbillies after performing tasks deeming them worthy of living. When they tried to leave, the trenchbillies followed SpongeBob and Patrick back home to the Krusty Krab. At the end of the episode, Mr. Krabs is soon hitched to Ma Angler.
One of the trenchbillies played a banjo so hard, he exploded.