Kyllo - Swenson - Kortegard - Neilson

I have recently taken on the search of my Mother-in-laws heritage and it has been very rough going. While she was still alive she had begun to find some information but it is not in a clear format. Her father possible went by several names in this order: Peter Kyllo Andrew Kyllo Andrew Even Swenson Andrews father, grandfather and uncle were: Arnt Kyllo Peter Kyllo Peter Kyllo Mother was Nikkolina Andersdotter Neilsen Kortegard I believe Nikkolina came to US from Christiana (place ?) sometime between 1882 - 1885. Basing this on the fact that her first husband died about 1882 and she gave birth to Andrew 1886. I am acquiring Andrews birth certificate to see if there is anything else to assist but in the meantime.. Suggestions on how and where to begin. So many of the databases I find on the internet for Norway are mind boggling.