When do stats get updated when training EVs? I know that new EVs are added to stats on level up, but when else?
And for emerald, do all stats get updated when giving an EV-changing berry, our just the stat corresponding to that berry?

If I recall correctly, the box trick should work - whenever you put a Pokemon into the PC, it will recalculate all of the stats based on the information.

I think when you apply the berry to fix the EVs, it will only look at the one stat.