I am not a teacher.
They do have different meanings, but they are not opposites. In the contexts given I would interpret them as follows.
'You may not pay me today…' = 'It could be/probably is the case that you are not paying me today'.
'You may not pay me less…' = 'You do not have the right to pay me less'.
'You may not go' usually means that you are not permitted to go. It could mean, in the right context, that it's possible that you are not going. If you want it to mean, 'You can stay here if you want', you should say, 'You may stay'.