Hi J.,
You are not alone! My son, who is 22 months, has done - sometimes still does - the same exact thing. When he's kicking during a diaper change, we've tried a few things. What works best with Cameron is to distract him. He's especially fond of snowglobes, so we have a plastic Curious George one that we'll shake up when changing his diaper. He's concentrating so much on making it snow that he forgets that he didn't want his diaper changed. We also try to make diaper changing fun. We'll take his feet and pretend to eat his toes - going mmmm, yummy toes! After a few minutes of that we ask him if he can eat his own toes. He's so busy grabbing at his own feet - keeping them out of our way - that kicking is not an issue.
As for the hitting, we'll grab his and and tell him no hitting - that it hurts Mommy & Daddy when he hits - in a stern voice and give him a warning that if he does it again, he is going to get a time out. Sometimes that works, other times, he gets the time out. We always explain to him in simple terms, at his level, why he is getting a time out, and tell/show him what is acceptable behavior. As far as the screaming when you try to stop your son from hitting - try to calm him down with breathing techniques. With Cameron I will take very exagerated deep breaths in and out, showing him what I want him to do. He'll eventually calm down and start breathing with me, or sometimes start laughing at me because I've exagerated my breaths so much. After that we'll talk about his behavior.
Just be consisted and show your son that you are in charge, not him. Don't be afraid of him crying - he's getting to the age of the temper tantrum, if he's not already there, where crying is inevitable. Just make sure he's in a safe place where he can't get hurt if he decides to throw himself onto the ground and start kicking and screaming. Sometimes kids just need a couple of minutes to vent. Don't you sometimes wish you could just scream at the top of your lungs. I've actually heard about studies done that have concluded that screaming at the top of your lungs is very successful in stress relief.
Good luck!