Is sealing my balloon frame walls with spray foam causing this musty smell?

Sealing the tops of those wall cavities in a balloon-frame house is actualy a standard practice for fire blocking and air sealing, but it is likely the direct cause of your new smell. In an old house like that, the walls basially acted as chimneys, constantly drafting air from the basement up into the attic. It was terrible for your heating bill, but it kept the funk moving. Now that you have capped those cavities, that century of dust, old wood resin, and moisture is trapped and leaching into your living space trough the outlets and baseboards instead.

The bigger issue is what they did to your attic ventilation. If they sprayed the attic floor and not the underside of the roof, your attic is still supposed to be a vented, unconditioned space. By sealing the gable vents, they have cut off the cross-ventilation. Those roof vents at the top are useless without intake air from the bottom or sides. You have basically turned your attic into a stagnant pressure cooker. When it gets warm, that heat bakes the old materials and the smell gets pushed down into the house because it has nowhere else to go.

You need to check if you even have soffit vents. Most 100-year-old homes in the Midwest do not. If you do not have soffit vents and they sealed the gables, they effectively killed your attic’s ability to breathe. You should probaly reopen those gable vents or install some kind of intake. An attic with high vents but no low vents just traps hot, smelly air at the floor level, exactly where your new insulation is sitting. Since the house is now much tighter, you might also need to look into mechanical ventilation like an ERV. Old houses relied on being leaky to cycle fresh air. You have stopped the leaks, wich is good for efficiency, but now you are living in a sealed box with a century of history. Run your bathroom fans more often in the short term to see if pulling some negative pressure helps clear the scent while you figure out the attic intake.

I never thougt about the outlets acting like tiny chimneys. My 1920s bungalow has those same drafty baseboards. If the OP seals the outlets with those little foam gaskets, whould that just force the smell out somewhere else, or does it actually help keep the 'funk' inside the walls?

I'm planning an attic project soon and now I'm worried about the same thing. Is there an easy way for a homeowner to tell if they have enought intake air before the foam crew shows up? I'd hate to accidentally seal myself into a smelly box.

Gaskets are just a band-aid. If you seal the outlets, the air just finds the next path like light fixtures or gaps under the trim. You really need to look at your basement or crawlspace too. In these old Midwest builds, if you didn't seal the rim joists down low, the house is still sucking in damp earth air from the cellar.

That "old house" smell is usally just damp masonry and dirt being pulled up into the wall cavities. Get a cheap hygrometer and see if your indoor humidity spiked. High humidity makes those organic odors ten times stronger now that the air is stagnant.