I finally managed to remove what seemed like a stuck stem, only to find something that seems rather odd to me. It seems to me like some merger of a threadless style stem with a threaded headset.

When I got the bike, the stem seemed fused since I wasn't able to adjust the height with the bolt loosened. I did some soaking with penetrating oil and finally got some side-to-side movement. Then I gave a few light raps to the bolt, thinking I was freeing a stuck wedge.

What I found inside was a sort of wedge that doesn't look like it was intended to be removed with the stem. Making me think it's not even intended to have adjustable stem height.

So, what do I have here and if it's an atypical stem, can I replace it easily with something more typical? Or is it still usable, as is, even if I knocked the wedge further into the fork tube.

Thanks!

Looks like a pretty standard threadless headset to me, unless I'm missing something in the photos. That wedge you've found in the steerer tube is a star nut, used to tighten down the top cap and sandwich the whole headset stack together.
A diagram from the venerable Sheldon Brown:

Once that star nut is installed, it's more or less permanent unless it needs replacing. So, you're right: this is not really intended to have an adjustable stem height.

Edit: I see now, that stem doesn't seem to have any pinch bolts, so the top cap is also tightening against the stem to keep it in position.

You adjust the stem height by moving the spacers above or below the stem. You just can’t raise the stem above the top of the steerer tube. If you need it higher than that maximum, you can buy an extension tube that goes into the existing steerer.

How does one tighten this stem to the steerer? I see no clamping bolts, nor split for clamping.

Does your stem have pinch bolts? I don't see them in the picture. What holds the stem to the steer tube?

Wow, it sure does appear to be a threadless headset. Thanks for politely addressing my lack of knowledge. I thought I knew what they looked like, but I guess I haven't seen one in the flesh, or looked at Sheldon Brown's exploded diagram recently enough.

Though, as [MENTION=362748]SquidPuppet[/MENTION] pointed out, the stem is rather odd. It doesn't fit with that I know of as a threadless stem. Maybe that's why I assumed it wasn't a threadless headest. I'll look again this evening, but I recall it being just a tube -- without pinch bolts.

It was very hard to remove. I don't know if this is original to the bike, I got it used. Possibly someone kludged things together.

As far as I know, Aheadset is a brand name that is linked with the concept of the threadless headset. It was apparently once owned by Dia-Compe. I think Cane Creek now owns it. I have a modern Aheadset threadless headset for one of my cheaper mountain bikes. It's an inexpensive headset with a plastic top cap.

https://www.aheadset.com/

The only thing that seems odd with your setup is the stem that doesn't seem to have any pinch bolts. You use the top cap, bolt, and star washer inside the steerer tube to set and maintain preload on the headset bearings, but the stem needs to also fix itself to the steerer tube to steer the bike. Unless this particular headset was designed for that top bolt to be set so tight that it essentially holds the stem in position? I don't think I've seen that before, but I guess it's possible.

The stem probably has a cinch bolt on the fork end of the extension (see pic), with an internal compression sleeve.

The only reason the headset acted like it was threaded, without the fork falling out, is because of the clamp style cable hanger.