Hi Robert, slow reply but hopefully it helps a bit...
Power for lift off = Literal translation is "ririku-shutsuryoku". However that word wasn't commonly used by the Japanese air forces during WW2. Most adequate translation would be "rishou-shutsuryoku". (Lit. translation = take-off and climb power)
Take-off power = Best match in the IJ air forces' language is also "rishou-shutsuryoku".
War emergency power = Literal translation is "sentou kinkyuu shutsuryoku" but again IJN/A didn't use such term. "Kinkyuu-shutsuryoku" or "sentou-shutsuryoku" would do(they were used like general noun... not official terms)
Rated Power = "Jouyoushou-shutsuryoku" is literal translation but that is not really rated power. "Koushou-shutsuryoku" should be closer to what rated power is.
Military Power = Literal translation = "Gunyou-shutsuryoku" but IJN/A didn't have such term for aircraft engines. "Koushou-shutsuryoku" would do it for this too.
Nominal Power = "Koushou-shutsuryoku" is literal translation but "jouyou-shutsuryoku" is more proper for it.
Maximum continuous power = Jouyou-saidai-shutsuryoku
Take example from Ki-84, its maximum power at sea level was "rishou shutsuryoku" with 1 minute limit. For Ki-61, 1 minute maximum WEP was commonly called "Chouka Buusuto(over boost)" by IJAAF pilots. But that's not official term and probably not the same with the plane's "rishou-shutsuryoku".
Robert wrote:
Also for our anyone who speaks Japanese:
How would you write these words in Japanese (with English letters)?
Power for lift off = ?
Take-off power = ?
War emergency power = ?
Rated Power = ?
Military Power = ?
Nominal Power = ?
Maximum continuous power = ?
Or what words did the Japanese use for these boosts settings?
Cheers and hopefully we shall soon see fully revised A6M's in Warbirds

!
/Robert