I live in the state of virginia. My husband lives in the basement, I did not know this is consider a separation. Since he committed adultry on me and I believe he still is, if I leave the house is it consider abandonment? Or can I leave and when the house is sold get my share?

If you want to leave then leave. In order to be legally separated though you need to file for it in court. Just moving away is not enough for it to be legal, that is just informal. When you go to court there should be orders from the judge about what happens with property and any assets as well as other debts that the two of you have.