Romaji is simply writing Japanese with Roman characters. Kanji Invaders reads Romaji input and converts it to Kana. This is done for maximum compatibility; normal English keyboard input is Romaji.
If a certain romaji letter doesn't seem to work for you, let me know and I'll fix it!
Japanese input methods require a special Romaji mode:
The Japanese Language Proficiency Test (JLPT) is an internationally recognized test of Japanese ability. JLPT defines five levels (N5-N1) of competency, with N1 being most advanced.
I've tagged the Kanji Invaders dictionary with approximate JLPT level information, so that you can study for a particular exam, or just select them all if you want lots of Japanese typing practice.
To change which kanji you're using, simply reload the game.