I'm writing a graphic novel with a segment in 1930's and 40's Japan. I've looked around but haven't been able to find any specific answers.
How would teenage schoolgirls have dressed at that time?
As always, the uniform would differ from one school to another school. But in the Showa period (1920s-1985) school uniforms is highly characterized by a strong influence from the military - especially the navy.
Japan had been in rigorous military transformation since the start of Meiji period (1868), and it is reflected in the education system it produced - on creating youth with a strong character.
While for the girls, the standard uniform is the nowadays popular sailor fuku (seifuku). It's a tad different from the contemporary imagery of seifuku though. It still has a clear navy influence.
It should be noted that from the 1920s to 1930s the girls school uniform is undergoing a transition from traditional Japanese clothing to a more European style. Some schools might still sport hakamas for girls in the 1930s.
You could see the transition here: http://archives.cf.ocha.ac.jp/en/exhibition/da/da0024-5.html And if interested, you may read a section from this book to read the social context: http://books.google.co.id/books?id=Nx-xX57pCicC&lpg=PA95&hl=id&pg=PA90#v=onepage&q&f=false