Our World in Data shows Japan as a graphable country for oil production going back to 1900. It looks like they get that data from The Shift Dataportal. They in turn appear to have gotten their data for the periods you are interested in from:
Etemad & Luciani for the period 1900-1980 Bouda Etemad and Jean Luciani, World Energy Production 1900 – 1985, ISBN 2-600-56007-6, Data digitalized and published with agreement of B. Etemad
FWIW, the result (reported on OWID in TWh) is roughly 4-3 for the duration of the war, which is dwarfed by the USA's 20,00-26,000.
I'm not sure the story here is very interesting, other than their production seems to have (unsurprisingly) dropped a bit as the war wore on. It never was a whole lot to start with though.
You'd think you might get a more useful image with the U.S. (producing at 5.5 times U.S.S.R. and 6.5. times Venezuela in the late 1930's) removed, but you don't really:
I found you pretty much have to remove everyone else to see any movement in the graph, that's how tiny it is. But if you do so, and adjust to only inlcude the immedite pre- and post-war era, you get this:
One could argue I suppose that their declining domestic oil production starting around 1940 may have been behind their desperation during that period to acquire more such resources abroad. But realisticaly, it was already so tiny that they had to be reliant on imports to satisfy their needs, and an extra couple of TWh here or there probably didn't make that much difference to their thinking. This is really just a noise graph.