Was this doing it before the new tires?
A vibration in the steering wheel at speeds over 50mph send off alarm bells to me. That is a perfect example of a bad balancing job on one of the front tires or possibly a bad tire itself. Remember, the people putting new tires on are not mechanics for the most part. This kid usually gets paid min wage or even per tire.
If you want to check your tie rods well, keep the car on the ground and crawl under enough that you can grab the tie rod. Have a buddy just turn the key to run, but not start. He will then move the steering wheel back and forth just enough that it is not actually going to turn the wheel but take up any slack in the steering (looseness). If you feel the tie rod loose, grad the outer tie rod end at the spindle. If it is bad there it will raise up slightly as the wheel is turned. If the outer is tight then it is the inner. Now you have a more expensive repair because of the alignment. An imbalance of the tires can wreck front end parts quickly.
Hope this helps
1992 Bonneville SSEi
White, grey Leather interior.
Tinted windows and blackouts on headlights.
Custom high flow exhaust, Everything replaceable - DONE
300 000 kms original engine, tranny 2 rebuilds.
Playboy Bunnies Embossed in Tint. Oh Yah!
Ever Seen a Polar Bear in a Snow Storm?