Deauthorize old user on my iTunes without their Apple ID
Yes! You can deauthorize any of the computers or devices authorized for your iTunes account. If you have access to a computer, the easiest thing to do is to open iTunes and go to Store -> View Account in the menus. (That is on my mac iTunes, it might be slightly different on Windows.)

In your Apple ID summary, you can see Computer Authorizations and Deauthorize All (you can easily reauthorize your own computers after this, since you have the password -- which you might want to change!) A little lower down you should also see "iTunes in the Cloud" where you can press "Manage Devices" to see the iOS devices authorized on your account and remove the ones you don't like.