This book started with the main character falling into the ocean, I believe. I also think he was in a battle in WWII. An alien empire has taken over The Earth and moved humans to planets named after the continents, except the humans didn't know they were moved. This future has a lot of dimensions where you can store your stuff, no matter how big it is, and retrieve it later.
Our hero, one of the more common superheroes, like Captain America or something and for the life of me I can't remember who, gets involved in the overthrow of this alien empire which is using Earth as it's capital. This is an older book as I read it somewhere around 2002. Any help is greatly appreciated.