My strategy for solving problems is always "divide-and-conquer" in which you localize where the problem is through tests that you create. The alternative approach is something like "test or replace individual components until it starts working again".
My first suggestion: Rotate the tires from front to back. LF to LR, RF to RR, like radials are supposed to be rotated.
While its not a conclusive test, it should give you a meaningful hint. I'd say if the steering issues go away, you probably have something wrong with those tires you just moved to the back. If it doesn't go away, you either have a bunch of bad tires or something wrong with the steering or suspension.
Also, while you are rotating the tires, you have the chance to take a closer look at the suspension and brake components, looking for breakage, wear or some other problem condition.
I hope this helps - its a cheap enough test. First of all, I'm cheap. Secondly, I'm lazy. If the two conflict, I often take the cheap option.