See my picture above ... I'm giving even odds that it's efflorescence or mold. I'm not quite sure. There's obvious past signs of efflorescence, but the substance I'm moving with my screwdriver looked a lot more like mold to me.
Anyway, I had a brickmason stop by and be kind enough to go over the project with me, and I'm going to be rebuilding some walls with a brick veneer from the inside. Which should be fun.
Here's a photo gallery of where we are now.
All the exterior walls need to come down and be rebuilt. Why? 'Cuz the sheathing is insufficient, always was insufficient, and there's nothing keeping water out of the walls now that the insufficient sheathing got bug-eaten, and water's coming into the house. I can't fix the whole house without knocking it down, but I can at least fairly cheaply fix this area.
I'm basically going to build, sheathe, and housewrap the exterior framing from the inside, and then tip it up against the brick and secure it in place, leaving a 1" air gap between the housewrap and the brick. The mason said that I shouldn't have to do much to secure the exterior brick wall on the first side I'm doing.
So I guess I have a boring PUT this week, but next week's will be fascinating.