Insulation Material – Identifying Types of Insulation and Sheathing Materials

The simple answer is "yes". Every piece of insulation you put in is a bit of heat that's not lost to the outside world. This is better for you as your house is warmer and your fuel bills are lower, it's also better for the environment as you're not using as much energy.

The more complex answer is "it depends". Buying and installing the insulation costs money (you don't say!) so the immediate equation becomes "is this cost less than the money I'll save over X years?". It's the answer to this that will, largely, affect your decision on whether to insulate or not.

The company who wouldn't estimate may be right (for their system) in that it would cost $2,000 (say) to do the work, but you'd only be saving $20 a year on your heating. This would mean it would take 100 years to pay back the cost. Now, if you can find a system that costs less then the proposition becomes more economical. Insulating the ceiling/roof space is a good thing to do anyway.

However, if your primary concern isn't the savings then you might decide to go ahead regardless.

A better question would be, why is my sheathing getting wet?

The grain of the sheathing suggests to me it is Homosote Homasote. It should not be squishy, rather firm and resilent.

Something is allowing water past your brick barrier, and then, past what was vapor barrier (for the time, 15-30# tar embedded felt paper. I would look up, overflowing gutters can get behind fascia boards and run down the inside of the bricks, soaking the sheathing if the vapor barrier was broken during the bricking (as sometimes happened, also mortar bridging can cause this). In no case is it normal for the sheathing to be wet. Poor tuck pointing (especially around windows) can also allow water intrusion.

Once the water intrusion is corrected, all stud bays in the affected areas should be opened and the sheathing evaluated for viability. Also, opening the cavity will allow faster drying out and possibly see where the intrusion is starting.

As an aside, my 1941 house used a gypsum lath board for plaster.