Those kinds of things, wood, furniture, and paint, can be affected by orange oil.
Before you start spraying inside the house, have you done what you can in the yard? Use beneficial nematodes, orange oil, and diatomaceous earth in the yard? Are you bathing the animals with the recommended shampoos? Any shampoo is going to kill fleas if you leave it on the animal for a few minutes before rinsing, but the library also mentions shampoos with tea tree oil or orange oil. Don't use too much of either of those, and don't use them straight on any animal.
Once you're sure you've dealt with the problem of the source in the yard, then look at the most benign treatments first, like puffing the diatomaceous earth in the house. Spray when you can't get rid of them another way, and test the dilute orange oil in a spot that doesn't show for the paint and wood and floor finish (someone else may come along with more information, but I typically use orange oil at the rate of a couple of ounces per gallon).
Good luck with this project!