What would be a suitable tag for houses of non-traditional construction such as BISF or Airey? What about Airey houses enclosed in brick cladding?
I would map them as normal and add building:prefabricated=yes, or building=demountable where appropriate. building:architecture=* can be used to described the architectural style (this may be wholly absent in war-built buildings 
).
It isn’t documented in the wiki as to how complete the building needs to be when it arrives on site for it to be counted as prefabricated. For example, is a modern timber-framed house where several / many large parts arrive ready-made from a factory ‘prefabricated’? Even when a crane is necessary for assembly?
You can use building:structure=* and description=* to explain the type of construction (that is, what stops the building falling down?).
Note that building:material only applies to the outer-most finish, with could be as thin as timber cladding or plaster
If a building has had substantial alteration, I use both year_of_construction=* and year_of_construction:rebuilt.