I am able to find 14 Elias Jonsen/Jonson/Johnsen/Johnson/Johansen/Johanson/Johannessen or Johannesson named in the 1865 Norwegian census. I looked for boys born between 1857 and 1859; given name beginning with letters 'Eli' and ending with 's'; last name beginning with 'Jo' and containing the letter 'n'. None of those 14 boys list a birthplace of Fredrikstad and none show parents with names like those you list above.
Try using the 'advanced search' option of the NHDC Norwegian census databases - you can alter the search criteria in any manner you choose and continue the search. (Important tip: the database WILDCARD is % and the instructions are offered are well worth your time to study.) http://www.rhd.uit.no/folketellinger/folketellinger_avansert_e.aspx
Jo Anne brings up a good point. We've seen others from Australia who have found very helpful information on Australian naturalization documents, those should be searched for by 'Conwill'.
'Conwill' - in another thread you were looking at a record for an Elias Johnson of an entirely different age category than mentioned above. How certain of his age are you?
It would be of interest to know where you got the info that Elias was born in Fredrikstad - and the approximate year - the names of his parents are typically swedish - Fredrikstad is close to the Swedish border - maybe he was born in Sweden and the parents moved to Fredrikstad?
Jo Anne brings up a good point. We've seen others from Australia who have found very helpful information on Australian naturalization documents, those should be searched for by 'Conwill'.
'Conwill' - in another thread you were looking at a record for an Elias Johnson of an entirely different age category than mentioned above. How certain of his age are you?