May and might can be synonyms. Here in the US it is more common to ask, "May I have a piece of cake?" instead of "Might I have a piece of cake?" Could is a possibility of doing something, may or might is asking permission to do something. When I was a child we would ask, "Could/Can we go outside?" The teachers would answer smugly, "I don't know, CAN you?" Well of course the answer was, yes it is POSSIBLE for us to go outside. But the teachers wanted us to ask permission to go outside which would be, "May/Might we go outside please?"