Question

For example: I have a Samurott and a weak, say, Dratini holding EXP Share. If Dratini/Samurott goes down, do they still get EVs?

Answer 1

No, if the Pokemon battling the opponent goes down, it does not recieve the EV's; the Pokemon that fainted the opposing Pokemon will recieve them.

Hope this helps =)

Comments

Adding on to this answer:
You ONLY ever get EVs when you obtain Experience points.

If you had switched in with all six of your party members and KO'ed an enemy, they would all get experience, and therefore, EVs.