Though I realize that we're talking about rifles that have been used by major powers in WW2, there's a few others that I think are still worthy of consideration. While Sweden remained neutral in WW2, they did send a number of their Mausers (M38s?) to Finland to help them fight the Russians. In either case, they are great shooters and I would highly advise against passing up a deal on one of these rifles just because they were not used by a "major power" during the war.
Similarly, a Swiss K31 is one of the finest milsurp rifles still available, and not too expensive to shoot once you've sourced some dies and brass (the bullet is .30 cal).
Funny how two of the nations that managed to remain neutral during the war also happened to have the most accurate rifles. Though sadly, it could be argued that the steady supply of the highest quality steel from Sweden, plus financing and munitions that crossed the Swiss border into Germany were a large (if not larger) factor as well. Neutrality meant that Germany was provided with vital supplies from two countries whose industries remained undisturbed by allied bombing right up to the war's end.
On a similar note, the M95 Mannlicher's and carbines were WW1 issue to soldiers of the Austro-Hungarian Empire, with many of them converted to the stronger 8x56R cartridge and put to work amongst a few of Germany's allies and as a second line rifle throughout WW2. Due to the extra effort required to source milsurp ammo or acquire the components to reload, some very clean or rearsenalled examples can sometimes be had for very reasonable prices.
Regards,
Frank
PS. Funny enough, like many of the other posters here, I too am lacking an Italian, French and Japenese rifle, lol!
PPS. I don't think that we should fault the Italians for not being diehard Fascists or their hesitancy to shoot their cousins from New York fighting on the other side. Similarly, the French issued millions of rifles in WW1 that were fired more than once and quickly picked up if dropped. It was a very divided country at the outset of WW2, with an army of older conscripts than most other powers due to the several million Frenchmen killed in WW1.