What is the difference between should and must and have to? How to explain using context clues (examples) to understand?

Should is weaker; it's used in advice. - Expected Result/Probability/Predictions/supposition

Must is stronger; it's used in orders. - Requirement/Strong Obligation/necessity/compulsion

Have to is a modal almost like, of must

He doesn't have to leave. ≠ He must not leave. The first one means he has no obligation to leave, but the second means he has an obligation not to leave

All the three are used to express 'obligation' but with different shades of meaning.

'Should' is used to mean "suggestion" and the action is left to the discretion of the person, meaning if the action is performed, it is good.

1. You should take regular exercises. 

It also means probability.

2. It's an off day today. George should be at home.

If it begins a sentence, 'should' refers a condition (meaning 'if')

3. Should you be late, give me a ring.

'Must' is used to express compulsion, meaning it is the only choice.

4. You must take regular exercises because you're putting on weight.

It is also used to express probability bordering on sureness.

5. It is an off day today. George must be at home.

Has to/have to are used to express compulsion arising out of force. There's no choice given.

6. I have to finish the work today. The deadline is approaching.

7. He has to leave right now!

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must order 

should for help or advise some one

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There is a difference between these words. Should means that it is a good idea to do something. It is more of a recommendation or an instruction to do something.

Must means that it is absolutely necessary that you do something. You don't have a choice in the matter and it is not a recommendation. It is a command.

The words "should" and "have to" or somewhat similar. However, "should" is more of a recommendation and "have to" is more of an obligation.

Should

Expected Result/Probability/Predictions/supposition

Stock prices should increase in the next few days.

Recommendation or Suggestion

He should be an engineer

Weak obligation/duty/propriety/necessity

I should work out more often

Must

Requirement/Strong Obligation/necessity/compulsion

Firemen must be ready for action at anytime.

Students who want to go to college must take more science courses

A Conclusion/high probability/conjecture/certainty/inevitability

He must not have been sick

Have to

Requirement/Strong Obligation/necessity/compulsion

Firemen have to be ready for action at anytime.

A Conclusion/high probability/conjecture/certainty/inevitability

He has to be a doctor [in reaction to his ability]

There is a difference between these words. Should means that it is a good idea to do something. It is more of a recommendation or an instruction to do something.

Must means that it is absolutely necessary that you do something. You don't have a choice in the matter and it is not a recommendation. It is a command.

The words "should" and "have to" or somewhat similar. However, "should" is more of a recommendation and "have to" is more of an obligation.