I have a 1994 Toyota Corolla. It has had a shimmy in the steering wheel for quite some time. Had a bent rim replaced, it has new struts, and today I had a new sway bar and links installed, as the sway bar and a link had been bent. The tires were balanced after the sway bar was replaced. Only have 124,000 miles on it. I can see and feel the shimmy in the steering wheel most when I'm going slow, but it's there at any speed. Also, at any speed, it's a bumpy/ride with vibration. I don't know what else is left to check! Oh, and my wheel bearings are all supposed to be fine, too. I've recently spoken with two other '94 Corolla owners whose cars have waaay more mileage on them, and they said they do not have this problem. It's making me nuts!!!

Get front wheels balanced and check ball joints

check for broken exhaust rubber mounts. check for broken wheel studs and bent rims and bearing failures

Probable front end suspension damage that has put the wheel alignment out . To need to replace the axle and rim indicates that the strut an lower support arm will also be bent. Have the front end inspected and a wheel alignment done

You've bent either the rim or the steering arms. You can't "straighten" the bent parts. Take it to a repair shop for part replacement. And soon before you have a steering failure and an accident.

Is the UPPER part of the Sway bar connected to the Chassis

All you need is a wheel balance. Either that or you have some mud or ice stuck in a rim, or it could be a bent rim.

The dealer is not going to replace something if they can not prove to the company the part is defective. The company won't pay the warranty claim.
A bent axle was my next guess. A garage could find out by using the same dial indicator used to check for a bent rim.
The dial gauge is placed against the shaft and the wheel is turned, if the axle is bent the dial will move.
I don't know what Road Forced balanced means, but most balancing machines duplicate road speed of about 30MPH. So a tire or wheel can balance ok on a machine but still have a vibration at speeds above 30 or 40mph. The easiest way to make sure is move the front tires to the back and see if the vibration travels too.
If you are describing the problem correctly, it almost has to be in the transmission, the axles, or the wheels. There is a slight chance a strut or strut mount could be faulty and allowing a small bounce to be amplified.

Hello. Welcome to FixYa.

Steering wheel tremble, or shaking, can usually be attributed to the fornt tires being out of balance, or, the tires themselves may be out of round, or, a rim could be bent.

I would suggest that you take the vehicle to a tire shop, and get the front tires spun-balanced. During that procedure, the tech will see if the balance is incorrect, the rim is bent, or if the tire is out of round.

Even if you have 'new' tires, an internal issue inside the tire could be the culprit.

Your best course of action is to get it to a tire shop, and get the above items checked out.

Thanks for choosing FixYa for assistance today.

brake discs not warped?steering arms ok (no play in them)bent stub axel check these things and you will find the issue

Remove the steering knuckle (remove center axle nut, wheel, brakes, strut, lower ball joint, tie rod end, axle.

Take knuckle to machine shop, with new bearing, and pay for replacement of bearing using hydraulic press.

Re-install knuckle.