So depressed due to my poor english.....

I would say "due to my work"

So, I need to communicate with all of them in English but due to my poor English, I find that I'm it difficult to understand what they are saying.

We never start a sentence with 'but'

It is fine when they are explaining the details of the project but it is so embarrassing when they ask me for somethings, but I don't know they are asking me, and hence then there is just have created some dead air.

I think "...when they ask me for something and I don't even know it“ would sound more natural. Also we also don't start sentences

When I notice that they are waiting for my response, I can only say something related to the project, but that may be that might not even be the correct response to their question.

I think "but that might not even have anything to do with their question" would sound more appropriate.

Hence, they just kinda laugh with some embarrassingly.... That make me so depressed after the meeting. I think I am looked so stupid in front of them.

So, I decide I should work harder to improve my listening and oral english.