Where do orcs get their weapons, armor, and other equipment?
Orcs can make some weapons, and seize others. They aren't rocket scientists, but the average orc isn't exactly Forrest Gump, either, and the smarter orc craftsmen are going to be able to function just fine, even if they won't be as cutting edge brilliant as the smartest human craftsmen.
Depending on the humanoid society, it's possible that older venerable craftsmen might be revered for their enhanced skill (although, in might-makes-right Orc society, not so much...). Lizardfolk and Troglodytes seem more likely to use this sort of technique, keeping their eldest hard at work crafting stuff for the younger, stronger warriors, capitalizing on their increasing expertise (and Lizardfolk, in particular, have been depicted in the past as having an 'advanced' caste, that is smarter and better-equipped than the 'savages').
Hobgoblins and Kobolds, on the other hand, are very organized and / or associated with craft, making them ideal choices for the 'suppliers' for Orcs, Goblins, Gnolls, etc.
The Kobolds are ideally positioned to act as weapon-merchants to the larger Orcs, as they can keep their forges and communities on the other side of tunnels and warrens that the Orcs can simply never penetrate, coming forth only to trade under conditions where the Orcs simply cannot storm in and take everything.
Since Kobolds, Goblins and Hobgoblins are every bit as smart as humans or elves, they can attain levels of craftsmanship every bit the equal of other races (although they lack the specific bonuses that a dwarf would have), and can provide gear, and even magical gear, as they can be effective wizards, clerics, sorcerers, druids and adepts as well.
Where do goblins get their weapons, armor, and other equipment?
Either they make their own, using their every-bit-equal-to-human intelligence, or Hobgoblins use them as peasant levies, and equip them accordingly, with cheap junk like spears.
Where do giants get their weapons, armor, and other equipment?
Hill Giants and Ogres use rocks and sticks. Frost, Fire, Stone, Cloud and Storm Giants are all well capable of making their own stuff. Fire and Stone Giants are probably the best craftsmen of the lot.
Hill Giants and Ogres being used by Fire Giants, Cloud Giants, etc. as flunkies (or Hobgoblins, etc. as mobile seige weapons) are probably better outfitted by their 'patrons.'
Where do demons/devils/devas/angels get their weapons, armor, and other equipment?
They have entire infinite dimensions, and, in some cases, cities the size of countries on the material plane. I'm sure there's a blacksmith somewhere out there working with that Baatorian Green Steel and Ysgardian Heartwire and making Celestial Armor and Demon Armor.
And, if they feel lazy, the Modrons and Formians are reknowned for their craftsmanship, and you can buy *anything* in the City of Brass, where thousands of Azer craftsmen toil endlessly to craft gear for the Efreeti nobility.
Are there non-PC-race smiths, markets, and cities?
Since we've seen them detailed in various adventures and settings, all the way back to 1st edition's Erelhei-Cinlu (an 'NPC race city'), I'd say yes.