You need to find more information about Edward in US records. Records such as the marriage record or application for a marriage license might list at least his father's name and perhaps WHERE in Norway he was born.
US censuses should give you information about WHEN he immigrated to the US.

The 1865 Norwegian census lists about 200 boys with names like Edward Pedersen/Pederson (and other spelling variants that must be considered) who were born between 1859 and 1861. Without you gathering more information who can tell which might be the correct match?

Elvine Helgesen is a rather unusual name and actually rather easy to find.
https://familysearch.org/pal:/MM9.1.1/NHC8-4Y9
Leaving from Oslo/Kristiania in 1891 -
http://digitalarkivet.uib.no/cgi-win/webcens.exe?slag=visbas...