PR gave you some excellent examples of things you can do (and need to) before you start searching in Norway. Where did they live in the USA? Perhaps the local county historical society has some information on them. Which state did they live in? And where? Their children had to fill out Social security applications, or their foreign born children's children, and on that application sometimes the place of birth for the parents is listed. It's easiest to start with the generation closest to you and work back, so find out everything about your father that you can, and work back from there. Start with his birth and death information, Social Security death index, etc.
The dates you have for them are good ones, because they would both show up in the 1865 online census, and also their emigration date might have them showing up on the lists of emigrants leaving Norway. But their common names gives too many results when searching.
don't give up, it is possible!