1. OD&D and Gygaxian 1e Were Too Weird to Live, and Too Rare to Die
One thing that I think often gets lost when discussing early D&D is how truly bizarre it could be. And the reason for this is that it wasn't "pure." It wasn't just Tolkien-esque high fantasy. Nor was it simply appropriated Howard/Leiber swords & sorcery. It wasn't extrapolated wargaming. And it wasn't the myths of a particular country.
It was all of it, and more. Because there were no particular preconceptions as to what had to be in D&D, or what had to be excluded. Where did your monsters come from? Well, anywhere! Little bit of Arabian mythology? Put in a djinn. Want to put in a little John Carter homage? How about some carnivorous apes, or giant white ones? Did you see some cool toys? Why not a ankheg, or an owl bear? Do you like 50s monster movies? How about some giant ants? Rakshasas, dinosaurs, critters from Japanese or Irish or Egyptian mythology? They were all fair game.
Everything was put into a blender, and became "D&D."
I miss this so much. So, so much.
These ideas were further explored in the overall weirdness that we saw in early D&D; early modules referenced dinosaurs, space travel, and parallel or pocket universes.
Time travel, different dimensions, space armadas, lasers, power armor, crashed spaceships, robots...there were robots on the wandering monster tables. There were creatures from Burroughs' Mars books...tharks, white apes, etc.
If you think OD&D and AD&D were weird, you should check out B/X and BECMI. Especially Mystara...and the Immortals rules in various incarnations. If you think OD&D and AD&D were weird...B/X and BECMI were utterly gonzo.
Mystara has a second, invisible moon with samurai cat people living on it. An ancient crashed spaceship. A buried nuclear reactor. An ancient Blackmoor device exploded, tilting the world. The Hollow World. The spell of preserving. Kalaktatla, the Amber Serpent...aka Ka the Preserver...an Immortal T-Rex who preserves ancient civilizations by moving them to the hollow world, including faux Romans and faux Aztecs. Flying continents. Flying cities. Crashed flying cities. Flying ships. Flying gnomes. A city of Immortals on the moon. Vast galactic empires. Time travel. Aliens. Genetic manipulation. Alternate dimensions. Thar. All the unique races and monsters. Immortals. Slowly dying magic. Shadow elves. The denial of the Hin. Bargle. Threshold. The Isle of Dread. The modules. I could almost swoon just thinking about it all.
3. Weirdness and 5e
This is where I get to the more interesting, and likely controversial, part of my general thoughts; what does any of this have to do with 5e?
Here's the thing- there are times when I feel that for some people, OSR (and OD&D / 1e specifically) is viewed as a reaction to 5e.
That would be odd as the OSR started at least a decade before 5E.
To put this in a more specific context:
In OD&D/1e terms, you might have a campaign setting that was generally medieval tech, but an individual might have a firearm or even a laser rifle.
In 5e, it is generally seen that the campaign setting itself would have to allow the specific tech for most DMs to approve it.
Well, in the older games it's still down to DM approval because the DM would have to put the high-tech item into the world for the PCs to find it. The player likely wouldn't ask for a laser sword or powered armor during character creation. They would be found in game.
In short, while I think that overall 5e has done an amazing job of incorporating numerous diverse cultural cues and viewpoints, the one thing it is not so great at is allowing the "weird" exception. Something which has long been baked into D&D's DNA.
There's a few more things WotC D&D has lost along the way, like zero to hero, fragile 1st-level characters, having to earn cool abilities, xp for gold, etc. Most of that's tweaks that can be put in or house ruled out, but the weirdness is definitely missing...and a lot of OSR stuff is almost laser-focused on delivering that content.