I'm from California with legal documents.
My partner, is Korean with an expired Korean passport and no other form of ID.
Can we travel by car together to different states like Nevada or Arizona?
There are technically no immigration controls between states. And I believe that police are not allowed to enquire about immigration status (because I think that is a federal responsibility).
However, there is one minor issue. Federal regulations give U.S. Customs and Border Protection (CBP) authority to operate within 100 miles of any U.S. “external boundary.” This means there is a 100 mile band around the inside of the US coastline and land borders in which the CBP can set up a stop and question you on your immigration status. See here for more info. This also means:
Two-thirds of the U.S. population, or about 200 million people, reside within this expanded border region, according to the 2010 census. Most of the 10 largest cities in the U.S., such as New York City, Los Angeles, and Chicago, fall in this region. Some states, like Florida, lie entirely within this border band so their entire populations are impacted.
I have encountered this in Southern New Mexico. The CBP has permanent immigration stops where they direct all traffic headed away from the border into an inspection station, and you have to be "inspected" by a CBP officer. In my case it was just roll down the window as I approached the stop, said "hi" and was waved through. But this is just my anecdata. Suspicious people1 may experience these stops differently.
Finally see here and here for a list of the stations that you will encounter.
1. With suspicious meaning "not looking like me"