Guy pulls your shirt. Grab your shirt and pull it back. If you don't have the ball this is a given. Or you can grab his back. And if you grab it, grab it. Don't tug it but give it a hefty grab. You could certainly use this tactic to slow him down and dart the other way.
Pushes you in the back. This usually happens when you box out well. So instead of pushing your butt back, chomp back with your heels and go after his toes. This isn't to disable the player, it is to give them something to think about. I can tell you I instinctively do this once I feel two hands on my lower back during a rebound.
Lazily keeps hand on your back at all times or when you have ball away from basket - to manipulate your body (and possibly tug jersey when you take off). This is illegal. Refs hardly ever call this on a smaller player. Chop theretheir arm right at their wrist with your off forearm as you swing around.
Pushes your body as you shot. To me this is one of the cardinal sins of intramural/pickup basketball. Guys give you a little shove and you don't move much because you are bigger - but your damn shot is always slightly off. The good news is for a person to do this they have to be playing your pretty close. I handle this while shooting. I keep two hands on the shot until the last possible second and push through towards the man. If they are going in to push my stomach they are going to get a face full of ball or elbow. The key is to start your shooting motion while cracking the other player on the chin.
always assume negative intent by the player. If a player does something "wrong" it isn't an accident - in fact there are hardly ever accidents on the court, even the "accidents" have degrees of intent. They have a mind and body just like you and you are not to be treated inferior because you have more of a conscience. If someone is so dumb that they truly don't realize what they are doing then you will only be able to rationalize through them with action.
always assume positive intent by referee. Most of the time the referee isn't calling things because they don't know better or they feel that it would interfere with the flow of the game. If a player has their hands on your back and it stops a spin move you should chop their arms away (any good basketball coach will teach you this). If the referee calls a foul on you don't overreact. Simply have a small conversation, "Sir, he had two hands on my back and pushed me. I know I fouled him but his hands were on my back for 5 seconds without a call." Sometimes the only way to educate a poor ref is to get fouls called on yourself - this is a long-term approach and obviously should not be played with a minute left in a game down 1.
whenever you play against a cheap player - make sure you are guarding the cheap player on the other end. It is a common ploy for a cheap player to hack the crap out of you and make sure you are not guarding them.
more than anything else - use the cheap player as motivation. Player Play harder and more aggressive the cheaper they act. This is a skill to bring your game up a notch AND stay under control. Player Play harder, not violent. Run the other player around on offense a bit. Bump into them.
all of the advice I gave you in the examples involves skill. The cheap player is skilled at playing cheap without getting a call against them. If you are truly skilled you can jamb your arm through his face while putting up a shot, knock him over, and draw the foul - all legally of course :). Everything takes practice and skill. I play in leagues in the winter that are about DIII quality of play that are crystal clean. Guys say sorry after fouling and so forth. I play in a couple of summer leagues that after a game it looks like I was attacked by a lion. It might take me a game or two or three to get my groove back in the retaliation department. It is a defined skill (you are getting outskilled there right now).