Check the US census enumerations (like the 1900,1910,1920) for details such as the year that they emigrated and/or when they were naturalized.
Look for newspaper obituaries (usually especially fruitful in small town newspapers).
Check for surviving church records where they were members of a congregation after coming to the US. Most Lutheran ministers recorded the locations where new members had been originally baptised and/or confirmed. Even if the name of the original parish in Norway is mispelled and 'Americanized' you'll have very valuable hints to research.
Ask every aunt, uncle and cousin for hints as to what part of Norway, perhaps aunt whosits says she thinks Carl was originally known as 'Karl Frisvoll' -- you understand, I'm just making up an example. Uncle whatsit remembers that grandma always talked of growing up on an island.... bits and pieces like that might help you in the long run.
Also check for any and all published histories of the county or small town where they lived or perhaps a centennial celebration publication of the church, sometimes 'prominent' or early citizens were listed with a brief biography.
Sometimes US naturalization papers will contain detailed nativity and/or US arrival information, land purchase documents, insurance, etc.