Jack D,
Before you do anything with the struts, you might want to make sure the fasteners on the strut mount and the strut shaft (center and larger than the other three) are tight.
Also the squeak you are hearing when you turn cannot come from the strut mount provided it is well tightened. The strut mount is made of two plates encapsulated in hard rubber to provide movement and dampening effect. The strut rod or shaft does not turn on the mount itselt rather it turns inside the strut body. For it to produce the squeak you described, the strut must have leaked all the fuid inside, bone dry and in a very very bad shape.
My 2 cents on your problem is a bad power steering pump or something getting in the way of your front tires when you turn.