Yes, @Poke J is correct. Gen 3 has no met date data, Gen 3 obtains a date when it's Pal Parked to gen 4. Gen 4's dates are its original obtain dates.
When transferred to gen 5, gens 3 and 4 will have overwritten dates to match the day it was transferred to gen 5. Gen 5's met date will be the original obtain date.
After gen 5, met data will stay the same and won't be overwritten. Transferring to gen 6, the only thing that's gained is a 3DS location, the 3DS data that transferred the Pokemon from gen 5 to gen 6. Gens 3 and 4 will have the date when it was transferred to gen 5, and gen 5 will have the date it was obtained. I don't know about the met level though, but I guess Bulbapedia says the met level gets changed from 5 -> 6?