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