Tore Kristofferson and his wife Marte Marie b Jakobsdatter left Oslo (Kristiania) on the 5. october 1883 by the ship Angelo. Their final destination is listed as "Apleton". Any suggestions on leaving harbour in the UK (Liverpool?) and what ship and date it would be natural to continue the travelling? To me they seem to vanish (in Hull?) but I'm a beginner at this field so I'm probably (and hopefully) wrong...
They arrived Philadelphia on 1883-10-22, sailing on the S/S Indiana from American Line. Departuring Liverpool. Marti Chesteffensen (65) Thore Christoffensen (67) Source: Philadelphia Passenger Lists, 1800-1945
"Apleton" would probably mean Appleton. There are/were at least 20 towns in the US called Appleton -- but the one which strikes me as where I have heard of Norwegian settlement would have been the Appleton in Swift County Minnesota. That would be my recommendation as a first place to check.
Their son Herman Thoreson (b 07 Jan 1844) can be found in Tordenskjold Township, Otter Tail, Minnesota (census-1880 & 1900). Herman emigrated April 23rd 1869, and married Hilde Jonethe in 1870. Census-1900 shows them with 5 children.