The most natural is "may."
Might/may is about permission, might more polite, but also more old-fashioned.
Could/can has been adapted to express permission, many don't think that's correct (it more naturally shows ability).
Read some of the postings by CalifJim in:
http://www.englishforums.com/search/advanced.htm?q=user%3acalifjim+might+could