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Check your tyre composition, it is possible that they have taken on form (shape) because of the odd manner in which you parked and returned to 'round' as they warmed up, nylon compound tyres are renowned for this.
Greg.

Once had Chinese tyres on my SE. They were very cheap and very hard wearing. They even had a small amount of grip - as long as the road was bone dry. And they were marginally quieter and smoother than driving with no tyres at all.

But the only time there was any steering vibration was when I managed to get a lot of debris on the insides of the rims (don't ask). Cleaned out the debris. Problem solved.

Could someone have hit one of your wheels with another car while you were parked on full lock?

Welcome to the forum. Your car deserves proper tyres and a full 4 wheel alignment from a specialist sporting suspension shop, not just any tyre shop.

Browse this forum for tyre choices and alignment shops in your area who are capable of doing our cars properly. There are hundreds of posts here about it all.

Couldn't find Zeetec.
If it is Zeetex there is no mention of nylon in the tyre construction,
but it is certanly one of the things nylon tyres are known to do.

nbse2 wrote:The car was parked with the wheels in full lock. When I drove off the front of the car had a serious wobble which started off at about 30km and just would not go away.
Today the car was ok. I am assuming leaving the car in full lock may have had something to do with it.

Being parked next to the kerb or another object which the tyres were touching with the steering at full lock while parked could also cause this.

nbse2 wrote:What I will do is actually purchase some new tyres for the SE. I had used Falken ZE912s in the past. From memory they were mildly noisy, but generally had no real problem with them in terms of grip (Made in Thailand). I have perused the site for recommendations, but any current recommendations on 205/40R17? If so would be appreciated.

Yokohama A.drive R1s. Not noisy. Grippy. Progressive and controllable. Awesome.

nbse2 wrote:What did you pay for the A Drives. I was thinking of the S Drives myself. Damn expensive though.

About $1,000 I think.

Toyo are good- if you check any of the major tyre fitters you will soon pick up whats available and in certain price ranges. Tyre specialists will also give advice and many will ask how the car is dríven. A tyre needs to be fit for one's purpose and budget including how long the product lasts- replacing tyres every 12 mths may not suit everyone.