• I haven't decided yet where to go on holiday. I may go to Ireland. (= perhaps I will go there)
• Take an umbrella with you. It might rain later. (= perhaps it will rain)
• The bus isn't always on time. We might have to wait a few minutes. (= perhaps we will have to wait)

• Amy may not go out tonight. She isn't feeling well. (= perhaps she will not go out)
• There might not be enough time to discuss everything at the meeting. (= perhaps there will not be enough time)

• I'll be late this evening. (for sure)
• I may/might be late this evening. (possible)

• I may go to Ireland. or I might go to Ireland.
• Jane might be able to help you. or Jane may be able to help you.

• If they paid me better, I might work harder. (not I may work)

The situation here is not real because they do not pay me well, so I'm not going to work harder.

• Don't phone at 8.30. I'll be watching the football on television.
• Don't phone at 8.30. I might be watching (or I may be watching) the football on TV. (= perhaps I'll be watching it)

• I'm going to Ireland in July. (for sure)
• I might be going (or I may be going) to Ireland soon. (possible)

But you can also say 'I might go / I may go ...' with little difference in meaning.

Might as well

Helen and Clare have just missed the bus. The buses run every hour.

Helen: What shall we do? Shall we walk?
Clare: We might as well. it's a nice day and I don't want to wait here for an hour.

We might as well do something = We should do it because there is no better alternative. There is no reason not to do it.

May as well is also possible.

• A: What time are you going out?
  B: Well, I'm ready, so I might as well go now.
• Buses are so expensive these days, you might as well get a taxi. (= taxis are as good, no more expensive)