The 17 basic techniques in Shodokan do have counters. It's a separate kata. There are some pictures off the york-aikido site should you wish to look at them.
However, you can use any kuzushi to break balance and once uke's balance is gone, you can do any technique out of the 17! It leaves you a _huge_ array of thigns you can do. When you are uke, you must try to keep your balance at all cost. Otherwsie, tori is going to make you fly using whatever he or she feels like it.
If your sensei is really against randori, then you can play with toshu. Ask a fellow student to pair up with you. One of you starts a technique, any technique. The other then must find a way to get out of it then he appilies a technique. Continue swaping roles for as long as you can. Try slowly at first and keep as relaxed as possible. It's not about throwing your patrner, it's about blending.