Hi lots of info. So are you saying this might be Edvard born 1870's dad and Ole's step brother has middle name of Edvard and that's how Edvard might have gotten his name ?
No Johan Edvard would be a sibling. It is a long shot as the occupation of Ole is not a sailor or fisherman and there is no connection to Kristiansund. But I am running out of ideas.
Here is the family in the 1865 Census on Furuhaugen
Maybe the Archives have sailor records from Kristiansund?
Even though none of the 12 Oluf in the census records was using Jonsen as his name, he could still be there.
And then there is DNA.
When you look at Edvards Baptism record you see 3 men with the same last name. Mother Guri Anna had a daughter in 1865 that was raised in Furset with father, Guri Anna passed away in 1879. Edward took the last name Jensen which was his his half sisters last name. Is Oluf his real name I think so. Jonsen I don't know. I will look for sailor records. I did look at your records for Oluf. Thanks for the help.