From what Ive Learned at Tech School:
To check tie rod ends for looseness, jack up front end, grab wheel at each side (9 and 3) on a clock and try to shake, if there is looseness, it could be your tie rod ends.
To check steering shaft looseness, ( the one that goes from steering wheel to steering box) grab it and gently move it around, if there is alot of play, it may be steering shaft u joints.
I would first start with the tire shake though.
Any play in the steering system will be multiplied greatly bby the time it reaches the tires.
another good thing ive found was to have someone turn the wheel and look at where the steering shaft meets the steering box, if the gear on the steering gearbox moves a little and the tires don't move at all, it might be your gearbox.
Sorry I started to ramble on
Hope this helps