Doh, maybe I should try reading whats on the actual wire
Regarding cross section and "does AWG size include plastic sleeve"
That depends on country of origin and specific standards that apply.
These days, AWG is only a standard size in North America, so anything using that gauge system should be optimised for that market.
Back in the day, B & S, SWG, etc, certainly in Oz, & I believe, more widely in Commonwealth,countries, referred to solid wire, like you might wind a coil or transformer with.
Stranded wire was identified by the strand diameter & number of strands, hence you found sizes like:-
23/0076, 7/010, 10/010, 3/029, etc.
In these examples, the strands were 0.0076 inches, 0.01 inches, & so on.
In most cases, you would work out the diameter require for a solid conductor to carry the required current, then add 10% for stranded wire, or do what most people do----- see what other people use in similar service.
In the real world you then have to use standard commercially available wire sizes, anyway.