The Japanese used three 7.7 cartridges. The one used in the rifle is the 7.7x58 rimless. Its base is close enough to the .30-'06 that the cartridges will fit in each other's clips, but of course the .30-'06 will not chamber in the 7.7 rifle. The reverse will work, though; I have fired 7.7 in a Model 1903 (under controlled conditions) and the Japanese clips work fine, even popping out when the bolt is closed. There was no sign of high pressure.
The 6.5x55 and 7.5x54 bases are enough larger than the .30 that they will not fit an M1903 clip nor an 8mm Mauser clip. .30 will fit (loosely) in a 6.5x55 clip and many of those clips have been sold for use in the M1903 rifle; some users even insist that the Swedish clip is the "correct" one for the M1903. That is not true, but they will work to an extent.
FWIW, when a rifle is loaded from a clip ("stripper" clip), it is not necessary to remove the clip by hand - pushing the bolt forward or releasing the bolt of an autoloader will cause the clip to "pop" out, saving reloading time. The only exception is the M-N and the Russian semi-autos loaded with the M-N clip; those clips have to be removed manually. AFAIK, the only Russian clip-loaded rifle whose clip "pops" out is the SKS.