Are the three D&D artifacts directly inspired by Thor's three artifacts?
Yes.
The synergistic relationship was established in Supplement 4 to OD&D (God, Demi-Gods, and Heroes, 1976, authors Ward & Kuntz, ed. Kask). This predates AD&D. Found on pages 23 and 24 is Thor's equipment that includes:
Mjolnir:
The magical Hammer of Thor. This hammer, when wielded by the Thunder God, will slay any giant it hits, and it never misses! Commonly the hammer is thrown and returns to Thor. Its range is not restricted as is the dwarves' +3 hammer and as long as there is a target in sight the hammer will hit.
When used in any other capacity besides the slaying of giants, the hammer will cause 10-100 points of damage. (snip the description of throwing lightning bolts with 2-24 d8 damage)
Megingjarder:
The magical belt of power. Combined with his magical gloves these items give Thor the comparable strength of a Storm Giant. When used by itself the belt merely raises the Thunder god's strength to that of a Fire Giant.
Thor's Magical Gloves of Power:
These unnamed items, when worn separately from Megingjarder, give Thor the proportionate power of a Stone Giant. As mentioned above, when the gloves are worn in concert with Megingjarder, Thor's strength is increased to that of Storm Giant!
Here's the problem: only Thor can use this hammer.
Only beings with a strength equal to a Frost giant may pick up and carry this item of power, (And that at -50% speed) and only Thor himself may use Mjolnir.
This hammer, when wielded by the Thunder God, will slay any giant it hits, and it never misses! Commonly the hammer is thrown and returns to Thor.
The intensity of the bolt is controlled by Thor himself. Lastly, the hammer shines a light blue color, thus warning Thor of imminent danger within 10-60 yards of himself.
What @Nagora cited (in a most excellent answer) is that in the 1e DMG, page 168-169, the first example of the player usable synergistic set built on this model: hammer, thunder (replaces Thor's lightning with Thor's Thunder, thematic consistency), giant slaying, belt and glove bonuses1. The synergy between belt, gloves and hammer mirrors Thor's set in a scaled down model for players to use found in 1e, but it retains an obvious thematic relationship to the God of Thunder:
High strength required
Giant Slaying
Returns to thrower
Thunder effect, stun, replaces 2-24 d8 (!!!) lightning damage of the divine model.
Points from the DMG 1e description:
Hammer of Thunderbolts
... a regular hammer of largish size and extra weight. It will be to imbalanced, somehow, to wield properly in combat, unless the
character has 18/01 or better strength and a height of over 6'.
The hammer then functions as +3 and gains double damage dice an any hit
If the wielder wears any girdle of giant strength and gauntlets of ogre power in addition, he or she may properly wield the weapon if the
hammer's true name is known.
When swung or hurled it gains a +5, double damage dice, all girdle and gauntlets bonuses, and strikes dead any giant' upon which it
scores a hit
When hurled and successfully hitting, a great noise as if a clap of thunder broke overhead will resound, stunning all creatures within 3”
for 1 round.
The last bullet is strong evidence of the linkage to Thor's hammer from the previous supplement -- Thor is God of Thunder -- as is the strength requirement: scaled down from Storm Giant strength(24) to 18(01) strength as a minimum to wield or swing. (Storm Giant Strength is from DMG page 145 in description of Girdles of Giant Strength).
When AD&D was originally published (1e), the "anti-Monty Hall" PoV expressed by Gygax, Kask, and other TSR worthies informed what came to us in AD&D.
From the Forward to Supplement 4, Tim Kask notes:
This volume is something else, also: our last attempt to reach the "Monty Hall" DM's. Perhaps now some of the 'giveaway' campaigns will look as foolish as they truly are. This is our last attempt to delineate the absurdity of 40+ level characters. When Odin, the All-Father has only(?) 300 hit points, who can take a 44th level Lord seriously?
Someone decided that the Thor's set idea was a neat one, but they didn't want mere mortals wielding a god's weapon: that would be too Monty Hall. Following that reasoning, the linkage between Thor's awesome set scaled down for a player character to use fits like a glove .... if not like an Ogre Gauntlet! :)
Thor's hammer has certain powers when in Thor's hands.
Thor's set adds synergy.
Mere mortals can't make it work, though perhaps a Storm Giant could wield it.
The Hammer of Thunderbolts is something a mortal can use.
A less powerful could be made if you found three independent items.
The template for the synergy is pretty obvious.
An inquiry to Rob Kuntz, Tim Kask, or Jim Ward (or other AD&D contributors) might confirm "of course we modeled it on Thor's item, it was X's idea" but with 40 years gone ... you might not get such an answer.
You might also get "Isn't it obvious?" as an answer.
The team at TSR grew with each passing year as success piled upon success. Whose idea was it first? Jim Ward's or Bob Kuntz? Someone else's with input to the DMG?
See p. 8 of DMG for a list of contributors:
Nonetheless, all are herewith credited and thanked, trusting that each
will know what his or her own contribution was!
Peter Aronson, Brian Blume, Mike Carr, Sean Cleary, Jean-Louis Fiasson, Ernie (the well-known Barbarian) Gygax, Luke Gygax, AI Hammock, Neal Healey, Tom Holsinger, Harold Johnson, Timothy Jones, Tim Kask, Rick Krebs, Len Lakofka, Jeff Leason, Steve Marsh, Schar Niebling, Will Niebling, Jon Pickens, Gregory Rihn, John Sapienza, Lawrence Schick, Doug Schwegman, Dennis Sustare, Jack Vance, James M. Ward, Jean Wells, and Skip Williams.
As to the gauntlets and belts:
In Monsters and Treasure, no such synergistic effect is found, nor in Greyhawk. The first synergy was for Thor's personal items in Supp 4. The lesser set's synergy arrives in AD&D First Edition (see Nagora's answer).
From Monsters and Treasure, OD&D Vol II, page 38: (OD&D before any supplements).
Gauntlets of Ogre Power: These gauntlets give the wearer the ability to strike as an Ogre and generally give his hands and arms the strength of an ogre. They do not necessarily increase hit probability however.
Girdle of Giant Strength: Wearing this device bestows the strength and hit probability (if greater than the wearer's own) of Hill Giant.
Note: Hill Giant Strength isn't enough to handle Thor's hammer, it takes a Storm Giant's strength to do it per supplement 4.
1 The purse never did match, nor the boots, thanks to fashionistas running amok in Lake Geneva!
