How do you stay at someone's house all the time, have sex with them, be romantic, spend evenings together, and still think it's ok to date other people?!?!? And the person you're doing that with is someone you were married to until two months ago and you lived with for seven years????? Again, WTFFFFFFFFF?????
Oh, Mrs. A, I feel the frustration in yoru post and can totally understand where you are coming from. As to why he lied and said he wasn't seeing anyone not long ago... cheaters lie. ALL cheaters lie. True facts.
I think you are doing well and should tell him you're not into being his sidepiece. I would probably advise telling him to move all his stuff out and go elsewhere to stay. Him staying with you is NOT helpin ghte issue. Right now he thinks he can have you on the side and as a crash pad (your home) while he goes out and dates/sleeps with other women. Note he said there were other women, not woman (Singular). Have you gotten tested yet??? Do it!