May/might, must,have to/had, can/could, should

MAY

We use may:

• when we are not sure about something in the present or future:

Jack may be coming to see us tomorrow.
               (= Perhaps Jack will come to see us tomorrow.)
Oh dear! It's half past ten. We may be late for the meeting.
               (= Perhaps we will be late for the meeting.)
She's had no sleep. She may be tired.
               (= Perhaps she is tired.)

• to ask for permission in a formal way:

May I borrow the car tomorrow?
May we come a bit later?

• to give permission in a formal way:

You may go now.
You may come at eleven if you wish.

• to say that someone has permission in a formal way:

Students may travel for free.

We can use may not to refuse permission or to say that someone does not have permission, but it is formal and emphatic:

You may not borrow the car until you can be more careful with it!
Students may not wear jeans

MIGHT

We use might when we are not sure about something in the present or future:

I might see you tomorrow.
It looks nice, but it might be very expensive.
It's quite bright. It might not rain today.

We also use might:

• as the past tense of requests with may:

He asked if he might borrow the car.
They wanted to know if they might come later.

• as a very polite way of asking for permission:

Might we ask you a question?
Might I just interrupt for a moment?

https://learnenglish.britishcouncil.org/grammar/english-grammar-reference/may-and-might

MUST

In general, must expresses personal obligation. Must expresses what the speaker thinks is necessary. Must is subjective. Look at these examples:

• I must stop smoking.

• You must visit us soon.

• He must work harder.

must not for prohibition

We use must not to say that something is not permitted or allowed, for example:

• Passengers must not talk to the driver.

HAVE TO/HAD TO

We often use have to to say that something is obligatory, for example:

• Children have to go to school.

In general, have to expresses impersonal obligation. The subject of have to is obliged or forced to act by a separate, external power (for example, the Law or school rules). Have to is objective. Look at these examples:

• In France, you have to drive on the right.

• In England, most schoolchildren have to wear a uniform.

• John has to wear a tie at work.

https://www.englishclub.com/grammar/verbs-modals-have-to-must-not.htm

CAN

We use can to make general statements about what is possible:

It can be very cold here in winter. (= It is sometimes very cold here in winter.)
You can easily get lost in this town. (= People often get lost in this town.)

We use can and can't to talk about someone's skill or general abilities:

She can speak several languages.
He can swim like a fish.
They can't dance very well.

We use can and can't to talk about the ability to do something at a specific time in the present or future:

I can see you.
Help! I can't breathe.

COULD

We use could to show that something is possible, but not certain:

They could come by car. (= Maybe they will come by car.)
They could be at home. (= Maybe they are at home.)

We use could and couldn't to talk about the past:

She could speak several languages.
They couldn't dance very well.

https://learnenglish.britishcouncil.org/grammar/english-grammar-reference/can-and-could

SHOULD

We use should mainly to:

• give advice or make recommendations  

• talk about obligation

• talk about probability and expectation 

• You should see the new James Bond movie. It's great!

• You should try to lose weight.

• John should get a haircut.

• He shouldn't smoke. And he should stop drinking too.

• What should I wear?

• They should make that illegal.

• There should be a law against that.

• People should worry more about global warming. 

https://www.englishclub.com/grammar/verbs-modal-should.htm