M.P.
I doubt that the fact he is a step son is the reason that he is hitting, etc all of the time. If this behavior came out only after contact with her it would probably be related.
Without knowing how you are teaching and disciplining him I don't know how to answer your question except to say that a baby/toddler has to be taught how to behave appropriately in a calm and consistent manner. He is behaving this way because he doesn't know how to behave any differently. He is NOT doing this to get on your nerves.
You do the same things that you would do if you weren't a step-mother. Unless you keep telling him you're his step-mother he doesn't know that you are any different than you would be as his mother. I wonder if you feel less entitled to parent him because you are a step-mother?
Have you and your husband, his father, decided on a way to teach and discipline? Have you read any information on ways to parent. I suggest that is the way to start. Do you know the developmental milestones of babies/toddlers so that you know what you can expect from your son? Do you have a daily routine that includes regular meals, snacks, naps, and bedtimes that he can predict to happen at close to the same time everyday? Would your home be calm and life predictable without your son's presence?
I think that once you have an understanding of what to expect from a two year old and some skills to direct his behavior you'll find that he will behave better. Even tho you are a step-mother it is up to you to teach him how to act. First you accept that he's just a little guy and love him as he is. You show him lots of love, praise him when he's being good, spend time playing with him and expect that he will misbehave and that this is OK. He's not being bad. He's letting you know he needs to learn something else.
I suggest that he's hitting, biting, scratching, slapping etc because he lacks boundaries and is angry at the chaos you describe. He doesn't know how to change it. I'm glad that you've asked how to do that. He cannot put you in time out. He cannot create continued chaos. You are in charge.
I suggest that you do some reading about parenting, child development, and discipline. I recommend Love and Logic for Toddlers and 1,2,3 Magic. I also urge you to take a parenting class. Many hospitals and community colleges give them. I sympathize with you. Your post sounds like you're at a total loss as to what to do.
If you would give some description of specific types of incidences I could give you ideas about how to handle them. Your post, tho sounds like there isn't an easy place from which to start. I feel overwhelmed in my effort to respond and wish I had more information.