Should употребляется когда даешь совет.
have to употребляется, когда обстоятельства вынуждают.
н-р:
1. You should read this book, it's very interesting. Тебе следует прочитать эту книгу, она очень интересная.
2. I have to leave the party , my mom has got ill. I have to call the doctor. Я должен покинуть вечер, моя мама заболела. Я должен вызвать врача. (обстоятельства вынуждают).
3. You should wash your hands before dinner.
4. I should lose some weight, I'm a bit fat.
5. You have to go there at once, you are waited for.
6. You have to tidy up your room, it's very dirty.
7. We have to read this book , as we'll right a composition about it.
8. We have to find a way out as we are in a difficult situation.