Is it legal to drive a trackday car on the road?

I was going to mention exhaust sound levels, but it appears that Oregon has an exemption for street rods, 815.107 : http://www.leg.state.or.us/ors/815.html If I were you I would print that page out, make sure you comply; and highlight your exemptions and keep in the car, just in case you get pulled over.

Contact the Oregon state department of motor vehicles or your local state police. The rules vary from state to state. In my experience the vehicle must have windows and fully operational doors to allow ingress and egress to the vehicle. It must be fully equipped with all safety features normally found on road vehicles and they must be fully operational. Track day cars must have additional safety features installed before they can race. I think you will find that the age of the car determines whether smog regulations apply. A car classified as an antique-25 or more years old, in some states releases it from compliance.

Check the rules in your state. Some states don't allow you to own a car over 25 years unless you have another vehicle. You may also want to get your local DMV to do an inspection; some body shops are also licensed to inspect vehicles. If the vehicle is registered its likely good but it may have been altered in a illegal way since the vehicle was registered. Also if your vehicle was illegally altered and you have an accident it may void your insurance.

sounds legal to me aside from smog regulations what type tires and exhuast system

If it's titled, registered and, insured. I don't see why not.