The first thing I will say is do NOT call the police on your son. He will end up with a criminal record and will likely resent you and be less likely to listen to anything you say in the future. As far as the syringes being a "friends", I can't tell you what a cliche that is. It's almost certainly not true. Who shoots up and leaves their rigs at a friend's house? Especially given all the other things you mentioned I would say it is almost certain that he is using.
As far as "making" him quit, since he still lives under your roof you still have some control over him. You can make it clear that drug usage is not allowed as long as he is living in your home and make him submit to drug tests to prove that he is not using. One thing I have seen friends' parents do in the past is make their kid's go to the doctor for suboxone and then watch them take it every morning. Suboxone will keep him from feeling withdrawals (it is also an opiate) but it will also block his receptors so that even if he shoots dope he will not feel a thing from it.
Personally I wouldn't recommend the suboxone route and as far as the drug testing it may or may not work in the short term but for long term sobriety he is going to have to want it for himself. My parents tried to force me to get clean tons of times and it never worked. There are ways around pretty much everything and you may end up pushing him farther away. Trying to make someone stop that doesn't want to might even be counterproductive since the natural response will be to push back against whatever you're trying to force him to do.
It's a tough situation you're in and I wish you the best of luck! Hopefully other people will be along with more advice shortly.