I have a Schengen Visa to Norway valid from the 26/10/2018. As a former student in Norway, I was invited for a conference that starts on the 24th. I called the embassy if my entry date can be changed and they said it was already stamped. Except I wanted to re-apply for a new one a have the old one cancelled. I do not have that luxury of time. So I have booked a flight from London on the night of the 25th that leaves at around 9 pm and arrives in Bergen by 11:40 pm. Trondheim is my destination so I will still wait at the Bergen Airport till 7 am the next day which makes me arrive in Trondheim by 8 am on the 26th. My problem is, will Norwegian airline let me fly from London on the night of the 25th and will it be a problem arriving in Bergen at 11:40? 20minutes before midnight (which is of course still a transit)as I do not step out of the airport until the next morning in Trondheim.
This will not likely work. There are very few flights to Bergen from non-schengen countries. Today evening, the only arriving flight is actually the 23:40 flight from London with Norwegian. Immigration and customs facilities are only staffed directly in connection with international arrivals and departures and you must expect to be ushered through immigration immediately after deplaning.
You can't expect that Norwegian will let you board the plane in London.
Checking through luggage when transiting from an international to a domestic flight in Norway has only recently become possible in Oslo. I doubt that the 'domestic transfer' concept has been implemented in Bergen. You most likely will need to claim your luggage in Bergen, go through customs there and re-check your bags for the flight to Trondheim.