IIRC, he started writing super science star smasher stories in the 30s as John W. Campbell - a few novels and a dozen or two stories - and then started writing more "thoughtful" pieces under the Don A. Stuart pseudonym from the mid-30s, which produced about a dozen or two more stories. He was one of the biggest writers of the era (probably with "Doc" Smith, Ed "World-Wrecker" Hamilton, and Weinbaum, though Weinbaum didn't do any star smashing).
After he became editor of
Astounding, in late '38 or so, he wrote another one or two - I think also a collaboration for
Unknown - but basically stopped as he could feed all his ideas to his "stable" and have them write the ideas for him.
I've only read
The Cloak of Aesir (collection),
The Best of John W. Campbell (collection, which almost completely contains
Aesir and has many more stories),
The Moon Is Hell (a pretty gritty story about trying to build a self-sustaining colony on the moon which also includes the
Unknown story), and
The Ultimate Weapon. I've also got
The Mightiest Machine and
The Space Beyond (collection) but haven't read them yet and just came across
The Black Star Passes the other day. That's an "Arcot, Morey and Wade" story and I think his other main series was the "Penton and Blake" stories which especially influenced Asimov.
I'm sure there's stuff on the web that can give you a more detailed overview, though.
I'm surprised you haven't come across things like "Twilight", though - a Don A. Stuart story that's in
The SFWA Hall of Fame, among others.