To wait means to pass the time until something happens:
– It’s 6:45. I’m waiting for the 7:00 bus.
– We waited in line for three hours to get tickets to the concert.
– You need to wait for the computer to finish updating.
Await is simply a slightly more formal way to say wait for. It is always followed by a noun:
– There are three projects awaiting the manager’s approval.
– I’m awaiting your answer.
– Everyone’s eagerly awaiting the release of the movie. or Everyone’s eagerly waiting for the release of the movie.
To hope means you want something to happen:
– I hope I’ll get a promotion this year!
– I’m sorry to hear you’re sick. I hope you get better soon!
– The traffic is very bad today. I hope I won’t be late.
To expect means to believe that something probably will happen:
– We’re expecting a visit from some clients – they said they’d come at 4:30.
– My boss expects me to arrive on time every day.