I think it would all depend on the United States to decide if they are going to ignore the sovereignty of Japan and force them to join the US as part of the landmass, as well as if they would give up their rights to California as a state (yeah right, sovereign soil so close to China? With such a strong military presence?).
California's power infrastructure instantly disappears, as it was part of the mainland US and now is an island nation. This creates a problem as the military bases protecting the California coast now have to defend it against incursion by China, Russia and whoever else decides they want a piece, from the far side of the new island. Gas generators only last so long and probably wouldn't last long enough for a complete rebuild of the infrastructure. Japan wouldn't see a loss so drastic, being part of the mainland US now, as well as being mostly self sufficient before the swap they should recover quickly.
The US mainland would probably opt to treat California like they do Hawaii, as a forgotten state. It's out there, but no one really cares. Unless they want to vacation somewhere a bottle of water costs $4.00. Meanwhile it pollutes the voting system of the mainland. I suppose it could serve as a stationing island for invasion into N. Korea, China, or Russia, but that's a whole other can of worms. Japan would probably want to keep their sovereignty, but they don't have much of a standing army just the defense force, and it wouldn't stand up to the might of the US military for very long, Especially given that one of the largest military ports that exists is in San Diego, and all those ships could potentially still be off the west coast. The US would have to adjust for over 85.5 million new people in it's population pool, after subtracting Californias population from Japans.
Trade would suffer, as nearly all of the imported products come through ports at Los Angeles (#1), Long Beach(#2), or Oakland(#10). Those ports now directly face the US across the Pacific, whereas the military force that faced across the pacific towards our enemies now faces us, and the unprotected border that faced Nevada and Arizona now face China, Russia, and Korea. Meanwhile the ports that support most of Japan's trade in Tokyo, Nagoya, Osaka, and Kobe are all now trying to scramble to make up the difference, and the militarized side of the island now faces Nevada and Arizona.
If the US military made any strong moves into positioning naval yards or military numbers on the new island state of California, someone would probably nuke it out of existence. Let's face it, the only thing keeping the nukes grounded right now is the fact that the US is so far away from the commie trio they would get early warning indicators. If the US had the military might they have in California less than 200 miles from S. Korea, the commie trio wold lose their collective (haha) minds.