Sounds like a perfect party for Murphy's World. If you can scare up a copy, you should have enough off-the-wall plot seeds to last quite a while. Stuff like (I'm going from memory, here) Bob, Lord of the Undead. Roll a random Murphy's Law every (in-game) day and punish the characters with it. Elves that are effete snobs and worried more about social climbing than making war on orcs. Giants that think the smaller races are "cute." Nodwick is another great source for gags/plot seeds.
In the main, adventures should just drop into the characters' laps with little to no warning (although with *these* characters, there should be plenty of backstory to exploit as well). Let the characters "have their head" for a little while, then dump a big, unavoidable plot hook on them.
Keep cycling between "free rein" and plot hooks, and never ever be afraid to reuse an underappreciated villain. You can always bring in clones, more-evil twins, or copycat villains if the originals die off. The more continuing plot threads, the better: it's easier to play a soap opera for laughs than standard D&D. Play it "bent," not "wacky"; prefer the pun over the pratfall and always let the characters have their comeuppance if they deserve it.
The more off-the-wall something is, the more straight-faced it should be played:
- Chauncy, in "alter ego" mode, is accosted by another "Lady of Mystery" who claims Chauncy stole his/her shtick. Who is this second "Lady of Mystery" and why does he/she seem so familiar to the other three characters?
- At some random time when buying equipment, the characters are being treated to the blacksmith's/shopkeeper's/whoever's "I remember when" story and, just when they are about to kill to relieve the sheer boredom, the storyteller's ancient foe muscles his way into the shop and starts a knock-down, drag-out fight to rival the climax of "Blade II." The characters can even participate if they wish. What level are the antagonists, and what is their beef with each other? Can the PCs solve it before the town is decimated in the crossfire?
- Shaggy and Scooby... er, I mean Tommy and Stony... get separated from the rest of the gang while looking for clues and come across a disused kitchen full of perfectly edible delicacies. Eventually, they have to regain their composure long enough to save Fred, Daphne, and Velma... er, I mean Chauncy, Uthress, and Heidi... from some trap in the monster's lair... and the monster turns out to be the groundskeeper in disguise. "And I would have gotten away with it, too... if it hadn't been for you meddling adventurers!" But what sort of treasure was the groundskeeper trying to chase everyone away from, and why must it be destroyed?
- One of Heidi's old rivals has also been beating, stomping, and headbutting, and now it's time for some payback. Who is the rival, and why is Baron Velcro paying a lot of attention to the outcome?
- In the "Hercules" vein, a god (avatar) crashes to the ground right in front of the characters, and immediately begins complaining. This god latches on to the characters and won't leave them alone until they've solved his/her problem. To get this albatross off their necks, the characters need to figure out what happened and try to mollify the god's angry rival. Luckily there's a temple nearby where the rival often sends an avatar. Will talking get the problem solved... or will the characters need to retrieve the Nectar of the Gods from the Bottom of the World, where the whiny one tossed it in a fit of pique?
- The characters are in an open-air marketplace in the Exotic East when an NPC adventuring group on flying carpets begins an assault. What is the prophecy they want to avert, and why do they think the PCs MUST DIE?
- Uthress has attracted the wrong sort of attention: important politicians, nobles, and other rich, hoity-toity folk keep asking her on dates! Why are the rich fawning over Uthress, and how does the sinister Doctor Plume factor into it?
- The tarrasque is loose! Luckily it's only killing the poor, while the rich watch the fun from afar, applauding periodically when the creature does something particularly entertaining. Who set the tarrasque loose, and will taking that thorn out of its foot help?
- A very old, very bored intelligent undead (the lich works best) is worshipped by a village full of brainwashed dimwits, but the entertainment value of it was short-lived. Lately the villain has been using the villagers to kidnap adventuring parties (after checking their resumes, of course!) so they can navigate a series of amusing deathtraps while the villain watches. Few survive. Can the characters provide enough entertainment? Can they come up with an idea for continuing entertainment that will be distracting enough to end the kidnappings and deaths?
- A group of halflings wants to go into business selling herbal products, but a consortium of druids approaches Tommy with a secret. What is this secret, and why are the halflings infinitely more dangerous than even they know?
Sounds like fun! I never had the guts to run a campaign like this, so I for one would like to know how it turns out!