They are actually very different from a dog or cat.
I've never heard of a road project lasting for months in the area of just one home to the point where tar fumes were prevalent the entire time. Sounds like a huge undertaking. I'm hopeful you will be able to get them out into fresh air and...
Hello and welcome to BYC! :frow Glad you joined.
I agree with @sourland. Try to find a space outside that they can stay for as long as possible every day until the dust settles.