Seeing as the walls are about 7 inches thick of 4 different layers of wood, is there much need to insulate?

Every pipe was ripped out, there were tons of holes in the walls, kitchens were damaged and old, you name it.  

Typically, the HOA is responsible for all repairs from the inside surface of the exterior walls outward and with party/common walls they would be responsible for repairs inside the two layers of sheetrock separating the units.

-Noticeable but not terribly strong pet odor throughout house, which according the guide, is considered damage...Things I'm not sure about:-Walls and doors are dirty in many parts of the house.

If you have multiple units on one system, and this being New England, I'm guessing it is an older building, you are most likely going to have to open up walls, and replace a lot of the supply and return lines so that they make home runs to individual boilers, etc that you will be installing.  

He gave me a quote (see below) for $6,000 - $25,000 depending on how good a fix I want with a summary of the problem as follows: "The structure has settled...the measurements indicate a drop that ranges from -1.9" to -0.4", with the average drop at 1.23"...the structure has sustained two severe foundation cracks...there is wall cracking on the inside of the home: cracks in the front room and cracks in the kitchen."

I painted ceilings, removed nails from the walls, and took off the light switch and plug-in covers.  

I have talked to a number of realtors in my area and these are selling well.Purchase lot $31,000Plumbing $15,200Electrical $10,600Concrete $15,800Dry Wall $12,760Flooring $4,000HVAC $16,158Lumber and cabinet package $66,976Driveway $3,200Landscaping $1,200Realtor fees when selling $13,000Bank fees and interest $4,100Building permit $1,700Labor to build - Paid to my construction company $36,750Total cost $234,344Going with recent history of what others are selling for in the area it looks like it should sell for a minimum of $250,000 possibly closer to $265,000.

Flooring and wall covering should have been removed to above the water level, along with anything that would retain water (e.g., insulation.)  

Just 2 days after posting this part of the ceiling and wall on one of my rentals fell down randomly!