After that Jorgen Von Strangle drank a can of Fizzy! soda, he got the trick-ups. So, he wasn't able to enforce the Da Rules, and pulled the "Conveniently Placed Family Locating Lever" to go to the nearest and available Von Strangle, and landed on the Turner's House. He wondered what was he doing there and called Nana Boom Boom on the video-phone, and found her busy playing Exploding Bingo, and she said his closest available relative was in that room, so Jorgen asked if it was his invisible cousin Leonard, but Nana said he was vacationing in the Bahamas. The next scene shows him in the Bahamas drinking a tropical drink, and Nana tells him his closest relative was Cosmo.
The limit to this invisibility power seems to be that it doesn't extend to anything in his immediate vicinity, such as his clothes. It is clear, however, that he sports a similar physique to Jorgen. If Jorgen and Nana Boom Boom are any indication, he would more than likely share their facial features as well, if they could be seen.