Your static objects still have collision events. So you can catch those events and rotate you objects by yourself.
The other way is: use dynamic body. But when add body to them set bounce to 0; so they won't bounce. And about Gravity, you can set gravityScale to 0 to make them don't react to gravity
Remember: static objects can't move or rotate by physics. You must do it yourself. And you can stop dynamic objects from bouncing or falling with gravity by setting 'gravityScale' and 'bounce' attributes
And more, if you don't want it to get pushed, catch collision event with right phase ( belongs to yours situation ) and set it linearVelocity to (0,0)
I haven't tried it before, but maybe you can make it a dynamic object but link to a static object ( likes a wheel link to a post ). So it can't move but still rotate when collision
P/S: I did a test and it worked. Make your objects like dynamic-balls and link them to static objects. They now can't move but rotate when collision.