[جواد عوض]

May or might can be used interchangably.
"I may go to the gym" and "I might go to the gym" mean the same thing.
It means that you are possibly going but have made no definite plans to do so.

I should go to the gym" expresses the need or desire to go but again does not say definitely whether you are going. It is the same as saying "I ought to go
"I must go to the store" is a more emphatic way of expressing the need to go.