I think there was a fleet commonality issue for Braathens with a mix of -200s and -300s, just as there was for Britannia until they inherited the Orion aircraft with the take-over. And the early 737-300s with B1 engines were not exactly long-range aircraft which would have limited Braathens' capability to do Norway-Canaries which they did with the later HGW 737-200s. Then again, I seem to recall Orion doing LGW-Tel Aviv with a B1 737-300!!
The OSL 737-200s were ordered by OSL and Britannia won a contract to fly them against other UK rivals. The arrangement was packed up by the end of Summer 1983 and Rank/OSL flew their passengers on the ex-Laker BCal Charter DC10-10s, later becoming Cal-Air and then Novair as a wholly owned subsidiary of Rank/OSL by that time. Novair had two 737-400s towards the end of its life (one of which went to British Midland to replace the aircraft lost at Kegworth), and one of the OSL 737-200s went on to Dan-Air as G-ILFC and then G-WGEL which stayed with them until the bitter end.