Skyrim Sidelines- Mind of Madness: The Best Kind of Dancing

The Northeast clearing contains a bed on which another Pelagius lies asleep.  Here, Sheogorath explains, you will have to fight the mad king's night terrors, freeing him to have a good night's sleep.  For some reason, that matters when you're dead.

Again, the Wabbajack is your only tool, so hit him with a blast from it.  This will summon the first nightmare, a wolf.  Turn the Wabbajack on it and it will convert into a goat- which Pelagius doesn't find terrifying at all, so that's fine.  Hit Pelagius again and you will summon a Bandit Chief, who begins attacking the sleeping Pelagius.  While bandits might not be terrifying to you (most of the time), the king is certainly afraid of screaming fur-clad men with axes hacking at him, so zap the guy and turn him into Little Pelagius- a copy of the mad king who is of the age where he had such nightmares.

Zapping Pelagius a third time will summon a Hagraven, apparently representative of- well, Sheogorath isn't entirely clear on that.  At any rate, another zap to the nightmare from the Wabbajack and a Sultry Maiden stands there instead, prompting joy from the young version of Pelagius that is still wandering around.  Finally, use the Wabbajack to summon Pelagius' fourth nightmare- a Flame Atronach.  The monster will flit around and attack you and Pelagius (both of them), so zap that with the Wabbajack as well, turning it into a treasure chest.

With all of his nightmares converted into things he likes, the deceased king's sleep is no longer tormented, and Sheogorath congratulates you on overcoming the man's fears.

Once all three clearings have been dealt with, return to the main clearing to speak to Sheogorath again.  Slightly disappointed, the Daedra of Madness sighs and holds up his end of the bargain, promising to return to where he belongs- inasmuch as the demented man can belong anywhere.  He does offer to let you stop by any time you're in the realm of madness, New Sheath, tempting you with a strawberry torte.  He then returns you to Pelagius' Wing even as he vanishes himself.

Returned to the palace, you can finally change back into your usual gear- though you do retain the clothes Sheogorath gave you.  Perhaps more importantly, you still have the Wabbajack!  The staff of the Mad Daedra projects blasts that do something random to their target- growth, shrinking, and conversion into anything from a rabbit to a cheese to a Dwarven steamwork are just a few of the possible results.  Remember, this isn't an offensve weapon, it's a tool of madness.