Dragan shaman is a decent 5th wheel too. He's got the permabuff aura, can restore players to half health outside of combat to save the healer some spells, uses metabreath attacks (especially Entangling Exhalation), and he can act as a backup for the frontline fighter or a bodyguard for the squishies. Very versatile support character, though not "strange".
In terms of the bizarre stuff you're asking about, I second the nomination of "Party limo" with a skilled scrier/teleporter. Having someone who "sees all, knows all, is everywhere and nowhere" always sounded like a lot of fun to me but I never got in a party big enough to try it.
Another option is an Enhanced Summoning Wizard who focuses purely on providing reinforcements on the battlefield - or extra transportation/utility outside of combat. At best, they're an additional damage source. At worst, they're great big meatshields that you can summon multiple of by using a higher spell (summon monster V gives 1d3 of a monster IV, and so on). It's a sort of exponential growth build, becoming significantly more powerful as combat drags on, but those first 2 or 3 rounds you are practically defenseless and need the rest of the party for protection.
