Should, Ought to, Had Better, Be Supposed to

Should and ought to are used to give advice or making recommendation. They have the same meaning (it is advisable to do something).
For examples:
• 'This soup is too salty!' 'You should / ought to send it back.'
• You'll catch cold if you go out like that. I think you should / ought to take a hat.

Should and ought to are also used to shows responsibility or duty.
For examples:
• People should / ought to be warned (= passive) of the danger of swimming off this beach.
• I should / ought to visit my parents more often.

We can use 'had better' instead of 'should / ought to' to say that we think it would be sensible or advisable to do something.
For examples:
 • If you're not well, you should / ought to ask Ann to go instead, (or ...you'd better ask...)
• You should / ought to have caught a later train, (not You had better have...)
• I don't think parents should / ought to give their children sweets, (not ...had better...)

We can use (be) supposed to instead of should / ought to to talk about an obligation to do something. It is commonly used in spoken English to express a' less strong obligation:
For examples:
• I'm supposed to be there at 10.00.
• The work was supposed to start last week.

We use (be) supposed to when we report what many people think is true:
For example:
• Eating sweets is supposed to be bad for your teeth, (not ...should be bad for...)

Reference

Martin Hewings (1999). Advanced Grammar in Use. A Self-Study reference and practice book for advanced learners of English

Permission: May, Can

We use 'may' and 'can' to give or ask for permission. 'May' is more polite and formal than 'can'.

• You can have a cookie after dinner , son!
• You may have a cookie after dinner, son!
• May I sit here?
• Can I leave early?

And we use 'may not' or 'cannot' to deny permission.

• You may not have a cookie after dinner, son!
• You can't cross when the light is red.

Prohibition: Mustn't and Can't

We use 'must not' (mustn't) and 'cannot' (can't) to talk about something you aren't allowed to do or you're strongly advised not to do.

For examples,

• You mustn't lean out of the window.
• You mustn't smoke in the bus.
• You can't cross when the light is red.

For strong prohibition we use 'must never'; for examples,

• You must never walk on the railway line.

'Must not' is used to talk about prohibition; however, 'don’t have to' is used to show lack of necessity.

For examples,

• We don't have to work on Sundays.
• I can hear you. You don’t have to shout.

Obligation: Must and Have to

Modals are special auxiliary verbs used to add extra meaning to the main verbs. Each modal shows different meaning in a sentence, for instance, ability, certainty, obligation, permission, and prohibition.

Form: Subject + modal + verb (bare infinitive)

Must and have to are used to show obligation, that is, something you're obliged or strongly advised to do.

Must is stronger and indicate urgency or stress importance. It usually comes from safety instruction or come from one of the speakers; for examples,

• You must fasten your seat belt. (safety instruction)
• I usually forget her birthday. I must remember this year. (from a speaker)
• The baby's asleep. You must be quiet. (from a speaker)

Have to is more commonly used. It comes from a third person, possibly from rules; for examples,

• The government says you have to do military service.
• You have to show some ID when you pay by cheque.

Advice: Should, Ought to, Had better

Modal verbs are used to express modality. To express advisability, should, ought to, and had better are used.

Form: Subject + should / ought to / had better + verb (bare infinitive)

Should and ought to have the same meaning. They are used to give advice, or say what is the right thing to do; for examples,

• You should /ought to call your friend to thank her.
• You shouldn't/oughtn't to tell lies.

Had better (or 'd better) has also the same meaning, but it's stronger. It implies a warning or threat of possible bad consequences; for examples,

• It's raining; you'd better take your umbrella.
• I have a very important meeting at 8; I had better not be late!

Modal Verbs

The modal verbs are: can, could, may, might, must, shall, should, ought to, will, would, and few other equivalents like have to and need to.

Position and form in sentences

• Positive: Subject + modal + main verb (infinitive without to)
• Negative: Subject + modal + not + main verb 
• Question: Modal + subject + main verb?

Usage

Modal verbs are used to add extra meanings – for examples, to show ability, possibility, advice, permission, or necessity … – to the main verbs.
 

1. Can

We use can to show

a. Ability

For examples,

• I can speak English. (Ability)
• She can't read Japanese. (Inability)

Note: We use can use the equivalent expression of " be able to " instead of " can " for taliking about ability or inability.

For examples,

• Phalla can speak English fluently.
• Phall is able to speak English fluently.

b. Possibility

For examples,

• Things can become more expensive next year.
• Piseth! He can't be our new boss.

c. Asking for permission  

For examples, 

• Can I smoke here?
• Can I take leave tomorrow?

d. Request

• Can I have a cup of tea?
• Can I talk to the procurement manager?

2. Could

a. Ability in the past

For examples,

• Sopheak could do maths tests well at school.
• She couldn't swim when she was 8.

Note: We use also can use the equivalent expression of " was/were able to " instead of "could " for taliking about ability or inability in the past; for examples,

• She could get the scholarship to study in Japan few years ago.
• She was get the scholarship to study in Japan few years ago.

b. Request (more polite than "can")

For examples,

• Could you please pass the report to me?
• Could you speak louder?

c. Asking for permission (more polite than "can")

For examples,

• Could I use your pen?
• Could I borrow some money?

d. Suggestion

For examples,

• I think we could go to a restaurant near here.
• You could try talking to our boss for help.

e. Future possibility

For examples,

• The corporation could plan to downsize next year.
• Many people could lose their jobs.

3. May

a. Permission 

For examples,

• May I take photos?
• May I sit here?

b. Future possibility (more possible than "might")

For examples,

• We may raise enough fund to start our company. 
• And we may have some technical problems for the first few months.

Note: We can also use the equivalent expression of " be likely to" instead of "may" for talking about future possibility. For examples,

• We may have some technical problems for the first few months.
• We are likely to have some technical problems for the first few months.

4. Might

a. Future possibility (less possible than "may")

For examples,

• We might have few customers at start-up.
• We might set lower prices too.

Note: We can also use the equivalent expression of " be likely to" instead of "might" for taliking about future possibility. For examples,

• We might have few customers at start-up.
• We are likely to have few customers at start-up.

5. Must

a.Obligation

For examples,

• All student must wear uniform.
• You must apply for a visa before going to a foreign country.

Note: We can also use the equivalent expression of " have to/ be required to" instead of "must" for taliking about obligation. For examples,

• You must apply for a visa before going to a foreign country. 
• You are required to apply for a visa before going to a foreign country. 

b. Necessity

For examples,

• It is 12:00 now. We must go now.
• I haven't finished installing all software. You must bring it back tomorrow.

Note: We can also use the equivalent expression of " need to" instead of "must" for taliking about neccessity. For examples,

• I haven't finished installing all software. You must bring it back tomorrow.
• I haven't finished installing all software. You need to bring it back tomorrow.

c. Prohibition

For examples,

• You mustn't drive on the left in Cambodia.
• You mustn't forget your passport.

6. Ought to

a. Advice (strong advice)

For examples,

• You ought to scan the virus before open the files. 
• You ought to see a doctor.

Note: We can also use the equivalent expression of " be supposed to" instead of "ought to" for taliking about advice. For examples,

• You ought to scan the virus before open the files. 
• You are supposed to to scan the virus before open the files. 

7. Shall

a. Offer  

For examples,

• Shall I carry the bag for you?
• Shall I pick you up tomorrow?

b. Suggestion  

For examples,

• Shall we go to Sihanouk Ville?
• Shall we launch a new project this year?

8. Should

a. Advice or recommendation 

For examples,

• We should solve the problems as quick as possible.
• I think we should check everything again.

Note: We can also use the equivalent expression of " be supposed to" instead of "should" for taliking about advice or recommendation. For examples,

• You should study hard.
• You are supposed to study hard.

b. Possibility (Assumption)

For examples,

• He should be busy at this time.
• Should you need something, tell me.

9. Will

a. Instant decisions

For examples,

• I am hungry. I will take you to a Chinese restaurant.
• "Where is the report?" - "Oh! I forgot. I will print it out now."

b. Certain prediction For examples,

• We will find a job after graduation.
• It will rain today.

Note: We can also use the equivalent expression of " be going to" instead of "will" for talking about prediction; i.e., when you have present evidence. For examples,

• It will rain today.
• Look at the sky. It is going to rain.

c. Offer and request 
For examples,

• Will you have a coffee? (offer)
•  I will have tea, thanks. (request)

d. Promise
 
For examples,

• I’ll do that for you if you like. 
• I won't tell anyone about this.

10. Would

a. Permission
 
For examples,

• Would you mind If I open the window?
• Would you mind if I brought a colleague with me?

b. Request 

For examples,

• Would you pass the salt please?
• Would you mind waiting a moment?

c. Suggestion
 
For examples,

• “Would Monday morning be OK for you?” – “That would be fine.” 
• I think the new software would work.

d. Invitation 
For examples,

• Would you like to go fishing this weekend? 
• I'd like to invite all colleagues for dinner today.

e. Preference

For examples,

• “Would you prefer tea or coffee?” – “I’d like tea please.” 

Further Reading
 

Betty Schrampfer Azar, Fundamentals of English Grammar, Second Edition, Prentice Hall Regents, 1992.
Betty Schrampfer Azar, Understanding and Using English Grammar, Third Edition, Prentice Hall Regents, 1999.