Is the lack of activation in sore calves indicative of a poor stroke technique? I know this is a funnily named question, but please bear with me.

The pain was new.

My calves were incredibly sore - it was painful to walk (Likely owing as I had to walk up stairs - I probably did more than 10 stories pacing a coworker literally half my weight among other issues.  I'm heavy.)

I couldn't rotate on my heels during my stride at all.

Despite this, my cycling was just fine.  I didn't feel my calves nearly as much as when I tried to stand up and walk!

How much should I be using my calves during my stroke?  I do have straps on my pedals.  Does the fact that they didn't hurt when I was making my normal cadence suggest I'm not using my calves as much as a cyclist should?

Thanks!
Basing workload or technique on soreness is a poor indicator of what is going on. You could have bad pedaling technique and never feel it or have great technique with no fitness and feel sore right away.

It's likely that you are not using your calf muscles as much when you cycle as when you do stairs. Stair running is a great way to train most of the muscles in the leg, and the extension/flexion coming from the edge of the stair is what causes your calves to be sore later. While I don't have any professional experience to back this up, I believe that cycling doesn't quite put your foot through the same range of motion, thereby activating the calf less(I suppose you could point your foot up and down more, but that's bad form).

What you are likely seeing is a comparison between two activities that use similar muscle groups in different levels. Example: pulling up on a pedal (with cage or cleat) is different than simply lifting your leg up to the next stair since the pedal provides some resistance.

My recommendation: rest it for a bit, maybe a day or two and then do both activities moderately and see if you notice any pain. If you do, consult a physician about it.