Moved to California from IL, have questions about registering my mopar in CA

not exactly correct. 75' and older don't need the inspection every 2 years.
technically the car is still required to have all the smog equipment in place, any after market parts need a CARB# and run within spec.

realistically a cop pulling you over for whatever, talking you into popping the hood, (i'd tell em' no thanks and stick to it), and deciding to send you to a referee station, should be your only problem.

http://www.dmv.ca.gov/pubs/brochures/howto/htvr9.htm <<<DMV INFO

good luck and welcome to cali

While I believe that is true. My experiance with DMV is they don't care about the smog if it's older than 1975 and they are not trained to even inspect it. That being said they may or may not want a vin verification and that can be done right at DMV by the person helping you if you have the car with you. They may also require some other safety inspection for brake and headlamps by a third party. However if the car is currently registered I doubt that will be required. As said already it just depends on who is helping you that day.

As far as anyone in California with a 1975 and earlier modified car. I personally would not consent to a engine inspection to any officer of the law. If they really what to see it they can get a search warrant. Once you get cited for a modified engine or tampered smog devices you will be in the system of Hell and trying to get your life back. Some departments have offices trained on smog equipment laws to deal with the fast and furious street racing crowd. Normally they leave us muscle car guys alone unless you are doing something totally stupid to attact attention.