The vehicle will have either one of two emission certifcations: CA spec or Federal spec (aka "49 state"). Most manufactures now just make their cars to CA spec and slap a CA spec compliant label on it, since most states have a similar standard and its no longer cost effective to sell them two different ways.
A new vehicle sold in CA must be certified to meet CA emissions. If you buy a new Avalon in another state that is not CA compliant, you cannot register it until it "ages": that is it must be two years old.
Since your 98 is past the two year limit, you can bring it into CA and it must meet the Federal standard for that year if a 49 state car, or the CA standard for that year if a CA spec car.
CA has the most stringent emissions tests in the nation, and in some areas of the state (typically urban) the standard is even higher still. Its not only a tailpipe test, there is also an underhood verification/functinal test. Your tailpipe emissions might be fine, but if you messed with the smog system from the stock configuration, it will not pass.
You can get smog check questions answered here:
http://www.bar.ca.gov/01_ConsumerAct...gChecknew.html