So I've been entertaining the thought of doing some character illustrations. To this end, yesterday I spent too much time on “research” to find out what gear the characters have. To save anyone else the trouble of having to figure this out, I thought it would be a helpful gesture to post my findings here. Please add and correct this list with your own knowledge, it'll help us all.
The episodes I looked into were the ones which memory served as being episodes which involved the characters finding (current) gear, or which had a character being introduced for the first time. These were episodes 1, 16, 19, 21, 23, 24, 25, 27, 48 and 53.
 “Sparklet” water-breathing necklaces. These are fine necklaces with a bead of water which slides along the length of the necklace with gravity, as a droplet would. This item is mentally triggered to have the droplet expand into a “water bag” around the character's head.
 Winter clothing, looted from a village in a snow environment.
Physical traits: Dwarf. She has some muscle (strength of 14 (2nd edition)). Her charisma is slightly above average at 13 (4th edition.. so I would venture to guess that the 2nd ed value is 12 or 13.) Don't be fooled by episode 1's suggestion that her CHA is 6, that's actually her wisdom. When they were looting the water world structure, Sarah clarified that Mildred's CHA is 13.
 War hammer gifted by Bahamut. This looks similar to her old war hammer, with familiar nicks etc, but refurbished. It has a new head.
 Plate mail gifted by Bahamut. This is a series of plates which cover only one arm, inclusive of her shoulder. It has a rail along the outside of her forearm, from elbow to wrist. A little disk is on the rail. If the disk is slid down and snapped in place on the outside of her wrist, a 4 inch, mirror-like disk appears. It has has an oil-spill, rainbow tint to it. This shield can be slid around onto her back or onto her wrist. There's some ambiguous description on the size of this shield... it's initially described as being 4 inches, and a few sentences later it is compared to a riot shield. I'm guessing that the “4 inches” is an initial projection, perhaps matching the size of the metal disk mechanism along the rails, and then it expands. But this is conjecture.
 Chain mail looted from a water-world structure. It is “brighter than it should be.”
 A fancy hat of detect lie. She hasn't normally been wearing this. I didn't find the episode where she acquired this (it was in the tower-planet I think), but I remember it as being very gaudy.
 A featureless, silver ring looted from the water-world structure. It is enchanted to help ranged attacks.
 A silver choker or necklace looted from the water-world structure. It is enchanted to help AC.
DAMIEN WORMWOOD DARKOMEN
Physical traits: Human. Black hair. Pale skin.
 His winter gear has dark tones, but not black. “Real dark brown.”
 A plain, 6 foot quarterstaff.
Physical traits: Half-elf. I don't know if you've heard, but he has a charisma of, uh, let me look this up here.. oh yeah, 19 (4th edition). Strength of 12 (4th edition.)
 A “pet” known as Stargoyle, gifted by Bahamut. It isn't clear yet if Stargoyle is Blackee's familiar, but the two are quite close. Stargoyle has the shape of a 1 foot tall gargoyle, but is featureless. It appears as a silhouette, filled with black space dotted by stars. It can hiss, chirp and meep; and is sometimes found perched on Blackee's shoulder.
 A rod of lightning. I didn't come across the description of this one.
 A “tuning fork”-like device, gifted by Bahamut. This has been attached to the end of Blackee's lightning rod. When the rod is activated, two lightning strikes are produced, one from each prong of the tuning-fork.
 A normal, low-quality dagger looted from the water-world structure.
 Supple, leather boots looted from the water-world structure.
 Runed, leather armor looted from the water-world structure. He has his normal clothing underneath.
 A normal, broad sword.
Physical traits: Dragonborn. Strength is “high”. Charisma is “low”. His manifest trait is breath-weapon rather than glide/flight, therefore he does not have any wings. Not any functional wings, anyway. Almost all dragonborn appear noble, as they are servants of the dragon god, Bahamut (one wonders why he and Sir Richard haven't talked about this.)
 A half helmet, gifted from Bahamut. This is a plate “jaw”, which clamps around the neck, and is of the same style as Mildred's and Richard's armor gifts. It has stylized teeth. There are two holes on either side of the jaw, which jet out some substance in front of Bart's mouth when he breathes, enhancing his breath weapon to be white hot, increasing damage and range.
 Skin armor, gifted from Bahamut. It looks like shed skin from a dragonborn. It appears thin and flimsy, but Bart can not rip it even with his strength.
 A short, purple robe which goes down to the butt, looted from the necromancer's treasure chest. Described as being similar to Lando's robe but with shoulders and a hood.
 A sword. Like other players, it's probably a broadsword, looted from various collector guards. I haven't confirmed this.
Physical traits: Human. VERY muscular, at a strength of 20 (4th edition.) His left hand and left leg are made of light, “You can only see the outline, there's no, like, shape to them. It just seems like they are made of light.”
 A single gauntlet which fits over his hand of light, gifted by Bahamut. The palm has a glass disk, which can focus the light from his hand into a 3 inch beam. The gauntlet has the same style as Mildred's and Bart's Bahamut armor.
 Chain mail looted from a structure in the water-world. It is polished to a mirror.
 Water elemental lord's crown. It is shimmering and spired.
 One of two, matching knives looted from the necromancer's treasure chest. The second knife was left on the party's crashed ship.
 A normal broadsword.
The party also took Amarthamon's special gear, in case a future party member ever needs it. His gifts from Bahamut were:
 A He-Man style harness, with a disk of metal over the chest. When thought-activated, micro-thin sheets of metal unwrap to cover his whole body.
 A great axe. It looks special.