Circa 1912 the normal wall construction from outside to inside would have been: 1)siding such as clapboard or shingles 2)vapor barrier such as tar paper or rosin paper (the pink stuff) 3)the sheathing, usually boards 4)the wall studs 5)the insulation (if any) 6)lathing (but only if the interior were to be plastered) or the interior wall finish.

Well, I guess my house isn't "normal" then. :)

Short of removing all the siding, any suggestions on how to seal it up now? Just put tar paper in the stud bays? I don't want to trap moisture anywhere, but I also don't want a breeze blowing through the wall.

What about that expanding closed-cell foam stuff--I think it's two part?

You could use DIY foam in place insulation, but if there are gaps large enough to see through to the outside, the foam will ooze out through them.

By far the best course of action would be to remove the exterior siding and the patchwork sheathing. Then put on sheathing in the form of OSB, plywood, etc., followed by Tyvek or similar product on the exterior side, then reinstall the siding. Since you're already down to the studs on the interior, this would not involve a huge amount of extra work. Once done, you'll have lots of options for insulating the bays between the studs.

Any other suggestions that don't involve creating a 500 sq ft hole in my house? I'm not removing 100 year old siding to "correct" their building technique.

so you don't have sheathing. you'll survive, i think. closed-cell foam insulation seems to be really your only choice. i found a couple of threads that might help

http://ths.gardenweb.com/forums/load/oldhouse/msg0410283024083.html
https://advice.thisoldhouse.com/showthread.php?t=7943

I'm not one of your gurus, so my input is a question: would there be any point in fitting maybe cut pieces of plywood between the studs? And then using rigid foam board for insulation?

Is closed-cell foam the expanding kind? I recently made some observations that have me pretty sure I won't use that stuff again.

When we did our interior renovation 18 years ago we sprayed expandable foam into some gaps around a window. We recently removed the window, and found quite a bit of green mold in the cavity. The mold was on the wood surfaces in a cavity that the foam had evidently succeeded in totally closing off, but it was also on the surface of the foam when we pulled it off the wood, so it obviously prevented the wood surface from drying. I'm guessing, therefore, that it would hasten wood rotting, quite aside from hosting mold.

KarinL

Having proper sheathing on an exterior wall is a good bit more important than "correcting their building technique." The sheathing is what prevents a wall from racking and is the second line of defense against exterior weather.

You can put whatever you want in the stud bays as insulation, but with gaps large enough to see outside, no sheathing, no Tyvek type material it will soon fail due to moisture and your wall will soon be just as cold as it was before you started renovating. Additionally, doing nothing on the exterior side will set up ideal conditions for rot within the wall cavity.

With all due respect, the house has stood for 100 years, so I'm not worried about it falling over. It has diagonal bracing cut into the studs - a very common technique before plywood.

It also hasn't rotted in 100 years. Unless I muck it up, it probably won't rot in another 100 years. The only areas that have water damage is where the prior owner mounted air conditioners in the windows and let them drip on the sills for about 6 months a year.

Really, that is my biggest concern. I don't want to do anything that ends up accidentally trapping moisture.