"May I" is a polite way of asking permission: "May I please have a cookie?" "Could I" is asking if it is possible for you to do something. Kind of strange to use actually becasue you are asking someone else if YOU are capable. "Could I eat that cookie in one bite?" "Should I" is asking somebody's opinion on if you should or shouldn't do something: "Should I buy the new car?"

may i go= 我准去吗， could i go? ＝我能去吗 我可以去吗 should i go?=我应该去吗

These words are called the attitude words used to express the speakers attitude towards people, events or information. MAY I : used for seeking permission to do something. Eg: May I come in Sir? COULD I : used for seeking permission to do something which is more polite. Eg:Could I use the phone. SHOULD I : used for asking whether it is necessary to do something. Eg: Should I pay any advance. Hope if you are in a real & serious search of a right English language practicing partner, here's to share my time with type or voice chat through skype only. I come forward to help you & meet me at [email protected].