The moves will simply take whatever type/category/power/accuracy it has in the game you are playing.
For example, Fire Punch is a fire move, so is always special in the older games. If you migrate a Pokemon with Fire Punch to a newer game like Platinum, it will become physical, because Fire Punch is physical in Platinum.
Same goes for the other stats. For example in Diamond/Pearl, Hypnosis is 70% accurate but in other games it's 60%. When the pokemon is in D/P Hypnosis will be 70% accurate and when its in Plat/HG/SS it's 60% accurate.