Correction: When can I use the words "can," "could," "should," and "may?"
CAN: "less formal / less polite than COULD"
>> Can I borrow your phone? -(Request / Informal)-
>> Can I join you? -(Asking for permission / Informal)-
>> Sure! You can sit next to me. -(Giving permission / Informal)-
>> That small dog can be very aggressive when threatened. -(Possibility / Something that may happen at a future time.)-
>> Can I help you? -(Offering something to someone)-
>> I can dance. -(Present ability)-
COULD: "more formal / more polite than CAN"
>> Dad, could you please help me with my homework? -(Request / More polite)-
>> Could I take the entire afternoon off? -(Asking for permission / More polite)-
>> I could have been the class president, but I quit during the campaign. -(Assumed possibility, somewhere in the past, that didn't happen.)-
>> You could order this dish next time. -(Suggestion)-
>> Mary could speak French and Spanish when she was in elementary school. -(Past ability)-
MAY: "more formal / more polite than COULD"
>> May I borrow your pen? -(Request / Formal)-
>> May I sit beside you? -(Asking for permission / Formal)-
>> You may eat some snacks during our class. -(Giving permission / Allowing something / Formal)-
>> It may rain this afternoon. -(Possibility)-
>> You may not enter the a private hunting ground for any reason without obtaining a permit from the Mayor's office. -(Prohibition)-
>> May you have many more birthdays to come. -(Wish for someone)-
SHOULD: "weaker than MUST"
>> You should be here before the start of the party. -(Obligation to someone)-
>> You should eat more veggies. -(Friendly Advice / Suggestion)-
>> Low-end smartphones in the Philippines shouldn't cost you more than a hundred dollars. -(Expectation about something)-