What are the differences in meaning, if any, in each group of sentences?
Here are my responses.
1. a. May I use your phone? = request for permission; formal style
b. Could I use your phone? = softened request for permission; informal style
c. Can I use your phone? = request for permission; informal style
2. a. It might not be Sally. = it's possible that it's not Sally, but I'm not quite so sure
b. It may not be Sally. = It's possible that it's not Sally
c. It couldn't be Sally. It is not possible that it is/was Sappy
d. It can't be Sally.It is not possible that it is Sally
3. a. I have to go = strong obligation or need
b. I should go. = weak obligation
c. I'm supposed to go. = weak obligation, probably imposed by someone else
d. I'd better go. obligation, often to avert negative consequences
Kis asks further:
What do the sentences below mean or imply?
1. She should have done well on the test.
Do we know whether she did well on the test or not?
There are two possibilities:
A. Confident expectation: Blanche took the test this afternoon, and I'm waiting to hear from her. She should have done well on the test, because she was very well prepared. (I don't know for sure how she did, but I think she did well.)
B. Comment on a past event: Katie told me the bad news. I'm surprised that she didn't do well on the test. She should have done well, since she was very well prepared. (I know that she did poorly.)
2. I didn't have to go to class yesterday.
I had to go to class yesterday.
Did I go?
We don't know for certain whether you went or not. Maybe you did, maybe you didn't. If you "didn't have to go to class," maybe you didn't go, but maybe you went anyway.
If you "had to go to class," you probably went to class, but you might have skipped it anyway.
3. I would rather have gone to the park.
Was I not able to go?
It's clear that you didn't go to the park, but the reason may not have been related to your ability to go. It's possible that you weren't able to go, but maybe you were able to go, but were persuaded to go somewhere else. Or maybe you didn't go because you decided that something else (less appealing) was more important, like taking your mother to the doctor or staying home and figuring out your income tax.