Advice needed/searching for Norwegian ancestors

I have searched for years on a segment of my family that comes from Norway. I have very, very limited information. I have a Peter Ellison who was born in 1810 in Norway, at some point he came to the US, ended up in Kansas and married an Otilla/Tilla/Matiilda Thomson/Thompson also from Norway. I believe I've found Matilda's parents in the 1850 census, Gunda and Jacobin Thompson. I have tried searching the main Norway database but get nowhere or get thousands and thousands of hits. I've not been able to find passenger records for the Ellison's or Thompsons. If Jacobin and Guna are Matilda's parents I know they arrived here between 1845-1850. Does anyone have any tips on now to search that may help? Thanks in advance.