NWL is a Line Traffic code. The LMR was split into three Lines for traffic purposes, WL, ML and NWL. Only the first two ever had locomotives "allocated" to them - the idea behind the allocation was that any diesel or electric loco could be dealt with at any depot on that "line". The concept and control arrangements were more suited to modern motive power so the scheme wasn't extended to steam locos or the NWL, where the main remaining steam activity was.
So if a loco was to be loaned out (or loaned pending transfer) to a particular "Line", I can see why it could be allocated NWL before gaining or reverting to a particular shed code. Usually the LMR would actually transfer a steam loco to a particular shed O/L so this is one I haven't come across before.
Inter is indeed Intermediate but it isn't a "service". Normal shed exams (a combination of days and mileage based tasks) were not usually recorded on BR History cards but works repairs and overhauls were. An Intermediate Repair is one type of "Classified Overhaul", carried out on a mileage/time basis - another one you might come across is G (or HG) - a General (or Heavy General) Repair. If you see C/L (or LC) or C/H (or HC) on the cards, these are "Unclassified Repairs" usually done at works - the C is for Casual and L or H is Light or Heavy. Sometimes you even might see an HI or LI instead of a pure "Int" or "Inter".
Sequencing of Classified Overhauls varied. Some would go G-G and some might be G-I-I-G or G-I-G or some would be I-I-I, the latter being mainly a WR thing as they maintained their engine components to a mileage interval standard and the final classification of locomotive repair depended on what repair the boiler actually got! Of course, if any loco had an out of course boiler change (which would be one of the reasons why HC or C/H would be used), that could really upset any sequence and also time between shops.
8F locos were mainly shopped in LMR days to Crewe, Derby, Horwich with some work being done at both Bow and Rugby. After the Workshops were taken into central BRB control ("the Workshops Division") in 1962, the regional grip declined and they started to be sent to other places like Darlington and Eastleigh.