I own a 2000 Lexus ES300 125k miles. My steering wheel vibrates when I hit about 60 miles or more. I do know that the owner put wrong tires on the car which are pretty worn on the inside (size 55 instead of 60).
The vibrartions while driving are 99% always when I am driving straight on the highway. The moment I turn the wheel to either direction it stops almost immediately.
Any advice? New tires, blancing, and alignment? Tighten the steering? Check the steering column for any defects?
What you described sounds to me like a good candidate for a wheels alignment. I would also consider a balancing of the tires as a second choice. If there is little thread left on your tires, you might want to buy new tires, which will give you a balancing at the same time. But I still would check the alignment.
Tires that do not wear evenly indicates that they are either under-inflated or over-inflated. A bad alignment will also cause that. As a last resort, I would have the steering column checked. Unless you notice a loss of power steering liquid, then it should be the first thing to do.