Death Is Cheap: Even cheaper than in AD&D proper. In the official AD&D rules, a character who dies can be raised from the dead by a living cleric. In this universe, a character who dies can be raised from the dead by any cleric, living or dead — including himself.
Descriptiveville: The main city on Central Earth — indeed the only city on Central Earth to be mentioned in any of the stories — is named "Town." Just "Town."
First Law of Resurrection: Even Sick Sword and Ringman, who were killed by having their souls annihilated on their alignment planes, which is supposed to erase someone from existence entirely, can come back.
Flat World: Central Earth really is flat. (If it were round, you'd fall off!)
Fluffy the Terrible: In The Intercontinental Proliferation of Disgusting Characters, Peter Perfect's paladin mount is an enormous undead dragon. He calls her "Fluffball."
I Call It Vera: With the exception of Prometheus and (snicker) Hymenslayer, every intelligent weapon seems to be named after its user: The Sick Sword, The Disgusting Dagger, The Ridiculous Hand Axe, The Gross (Broad)Sword, The Unbelievable Long Sword, etc..
Ice Cream Koan: Koenieg tends to spout these. He is a druid, after all.
Wierd Dough turned to the Great Druid. "Don't you see what they're doing?"
"All things must exist in balance," Koenieg replied.
"First torture and now a gang-bang!"
"The Way exists along the golden path," Koenieg continued.
Implausible Fencing Powers: Sick Sword, while locked in mortal combat with Omnion, gives Omnion corrective eye surgery with a few sword slashes.
Infinity+1 Sword: In the never-written epilog, it's explained how the random magic item tables in the 3rd Edition Epic Level Handbook can allow a weapon or a piece of armor to keep increasing its plus without limit. Unbelievable Sword literally has a +infinity sword.
Everybody else: "Oh no! They can do more damage that way!"
Medium Awareness: All the characters are aware that their universe operates under AD&D rules, and have access to all the rule books.
Munchkin: Every disgusting character. Every single one of them. If the author had heard the term "munchkin" at the time he wrote IUDC, he'd have used that word instead of "disgusting character".
My God, What Have I Done?: Gross Sword's basic reaction at the end of The Sick Kids. Pity he needed to be reduced to 1 hit point first.
Ninja Pirate Zombie Robot: Ridiculous Sword's +6 holy vorpal defender frost-brand flame-tongue sun luckblade of wounding, dancing, life stealing, disruption, slaying everything (as in the arrows of the same name), throwing, thunderbolts, red blue green black white brass & copper dragon slaying, speed, final word, and nine lives stealing with maximum intelligence, eight special purposes, and enough artifact powers to leave her set for life.
In his original hybrid 1st/2nd Edition incarnation, Unbelievable Sword was an Assassin, Monk, Druid, Barbarian, Oriental Barbarian, Bushi, Fighter, Thief, Bard, Wu Jen, Thief-Acrobat, Sohei/Ninja, Cleric, Illusionist, Abjurer, Conjurer, Diviner, Enchanter, Necromancer, Transmuter, Invoker, Weapons Master (a fake class made up entirely for the IUDC stories), Yakuza, Ranger, Shukenja, Cavalier, Anti-Barbarian (identical to a Barbarian except lawful instead of chaotic), Kensai, Paladin, Samurai, and Magic-User.
Overshadowed by Awesome: Ringman is 9th level, has 18/92 strength (equal to 22 strength in 3rd or 4th Edition), wears +5 plate mail (or +4 full plate, depending on which edition of the rules are in force at the time), carries a +4 shield, and wields a +5 Holy Avenger longsword. By most counts, he would be a very powerful paladin — but he pales in comparison to the disgusting characters.
In the pocket multiverse dungeon (3rd story, chapter 12), he worries about hidden traps with vorpal sword machine guns, rapid-fire sphere of annihilation cannons, or spring-loaded sword-of-sharpness-firing ballistae.
Psychic Powers: Both 1st and 2nd Edition AD&D rules allow a character to have psionic abilities without having to sacrifice any power in their normal character class(es). Thus, all disgusting characters have them.
Rules Lawyer: Every loophole and unanticipated contingency in the AD&D rules is exploited.
For example, when Ridiculous Sword hurtled toward the ground at nearly the speed of light, she took no damage when she landed — because she happened to land next to a castle's outer wall. She had monk as one of her classes, you see, and monks in 1st Edition take no damage when falling within 8 feet of a wall. If she had pressed the point, she could have insisted that arrows and fireballs couldn't hurt her during the fall either, because the rule says a monk can fall "without taking damage" if (s)he falls within 8 feet of a wall.
When a cube of frost is active, the space inside the cube is always 68 degees Fahrenheit, but the cube can only absorb so much cold damage before it fails. They can use this to walk through molten lava or even the interior of a sun unscathed.
In 2nd Edition, the scarab of protection gives its posessor a saving throw against spells that normally allows no saving throw. In 1st Edition, though, this is phrased as a saving throw against magic that normally allows no saving throw. "Magic" could theoretically mean any magical effect hedged out by an anti-magic shell, including the powers of all magic items. You could get a saving throw against the decapitation effect of a vorpal sword, the slaying effect of an arrow of slaying, etc..
Orphaned Series / Dead Fic: Union was written entirely in 1986. Sick Kids, in 1988. The author wrote the first page or two of Proliferation in 1989, then put it on the shelf until 2000 when he discovered the Hungarian translations of Union — this inspired him to start working on Proliferation in earnest. He wrote all 12 chapters of Proliferation, but has never ever managed to finish the Epilog in all that time. (The Epilog now contains author's notes about what he intended to have happen.)
Stat-O-Vision: In Part 3 of The Sick Kids, Ridiculous Sword pulls Jimmy's character sheet out of thin air, and critiques him on his ability scores.
World of Badass / Everyone Is A Super: In The Intercontinental Proliferation of Disgusting Characters, the word has gotten out as to how all the Disgusting Characters got so disgusting so easily. Now, everybody and his brother is a Disgusting Character.
Why Won't You Die?: The pocket-multiverse red dragon bellows this, being completely unable to harm Unbelievable Sword despite attacking all-out over and over again (while Unbelievable Sword ignores it to rant about something else).