Speaker placement in strangely shaped "room"?

No question about it. There is no formula for odd shaped rooms. Or much for any other rooms in my opinion. Research the Sumiko Master Set method. The speakers will "play the room". I've never found a better starting point. It was developed for hotel and meeting rooms for hi Fi conventions. Imagine how hard that is. If you spend the time and are careful you will be rewarded. Forget the tape measures, laser pointers, RS meters, hand clapping, and calculators.

You really need to provide dimensions, we are not mind readers.

For ex. If you have 15' wide by 25' long you wouldn't need to worry about corner placement because you could use the long wall method.

Kind of hard to tell how much space there is to work with since no distances are provided. One thing I would look into is a diagonal set up where you could leverage the solid wall space between the door and corner A and corner A and junction B.

What kind of room is this anyway and why does the wall stop short of the floor?

There's really no way around it; you're just going have to experiment with placement. I wouldn't assume that you are going to get bad sound. Sometimes with an odd room, you can get lucky and have no problems.

If you run into some problems, here's something you can try that's not too expensive. Most room tuning treatments are made out of fibreglass. You can make some very good ones yourself. All you need are pre-made fibreglass panels (not the big rolls, but the kind that look like pictures that can be hung on the wall.) Wrap them in a fabric that matches the colors in your room, and that's it. Just put them where you need them. For your room, you may want to mount them on some type of stands and simulate a wall on the left side of the left speaker. Hopefully, that will give the speakers some balance and help with imaging.