"Expect" is the strongest; if you expect to see someone, you are sure of it happening.
"Ten o'clock on Tuesday is the best time for me to come in for an interview."
"Great. I'll tell our personnel director to expect to see you then."
"Look forward" implies that the event will take place, and also adds the information that you will be pleased by its occurrence.
"I called to say that Katie and I will be at the party Saturday."
"Great! We'll look forward to seeing you then."
"Hope" means that you wish it would happen, but can't predict whether or not it will.
[to answering machine] "Charles, this is Del. I just wanted to let you know that I'm having a few people over for dinner next Saturday at eight o'clock. Hope to see you and Katie then."
"I'm going to Paris next month. I heard Tom was living over there now - I hope to see him while I'm there."
[not a teacher]