OK, you asked "how should I deal with this?" not "should I stay with this man?" so:
A) Boundaries. You are going to need them. Check out the captain awkward blog, go on an assertiveness course, read some books.
B) Don't become financially embroiled with this man. Do not move in with him, buy shared items or get a joint account. Under no circumstances ever lend him money. When he asks (he will) your line is "I'm afraid my budget won't stretch that far - all my money is earmarked for things my son and I need".
C) Use barrier protection for sex. This guy will continue to sleep with other people so you need to protect yourself with condoms. A backup method to prevent pregnancy would also be a good idea.
D) Do not allow or encourage him to act like a stepdad to your son. It will only give you another excuse not to address any bad behaviour from your boyfriend - "but my DS loves him so much!!" etc. Keep him as your boyfriend, not someone you get your kid all mixed up with.
E) Did I say don't lend him money? Don't get pregnant either.
F) Stay out of his relationship with the mother of his child as much as possible. He can rant to other people about what a bitch she is, how unfair it is, etc. When he is with you, he can talk about all the other aspects of his life that aren't his ex partner.
G) OP, be honest with yourself. You know this man to be a liar, a cheat, a manipulator and a weasel. Never forget that he lies to you and cheats on you - filter all the information he gives you through that knowledge. If all you have to go on is his account of something (Eg he is the one saying his ex is crazy, wants him back, is doing it for revenge, etc) then always remind yourself that he is a proven liar and cheat, and make your judgements accordingly.
Put yourself and your son in front of him.