Tell the squatter to get out immediately or you will take them to court for the unpaid rent, utilities, cleaning, damages, court costs, attorney fees, and everything else.

I would say the biggest things to look at would be do you want replacement cost (amount needed to replace/fix at todays cost) or actual cash value (depreciated amount depending on age of roof, or item damaged).

This was tenant damage during their tenancy.  

If the properties are for sale, they have a price.Regarding buying rental with S8 tenants in place, you need to verify the following so you don't get scammed:1) Rent amount2) S8 / Tenant split of rent payments3) What utilities tenant is responsible per HAP contract4) Any security deposit (which is for damages, NOT unpaid rent).

Check for water damage or signs of flooding, as certain areas might be prone to that.

Despite the contract clearly stating that Bridgehouse would pay us rent regardless of whether tenant pays them, Bridgehouse taking care of all damages to property....we have not received any money from Bridgehouse.

Anyone make them understand real estate valuation and the damage they are doing?

That may take a while to get them out, and they may cause damage before they leave. 

There was some minor damage to the ceiling and the AC vents.

The best part about the housing authority is that there is a guaranteed payment, and they have programs to help with any tenant damages upon move-out.