Start with this question, which is close in meaning, "Why should we listen to you?"
The insertion of "the hell" is a way of intensifying a question, making it more obvious in this case that the questioner thinks there is no reason to listen to this person. Let's put that in () and change the sentence a little.
Why (the hell) are we supposed to listen to you?
The red bit implies that we do not have a choice about listening to this person. Most likely, given the previous statement, this person is a teacher and the speaker is a student.
Why the hell are we even supposed to listen to you?
Including the blue even adds a touch of scorn. It suggests also an implicit preceding statement - so with a bit of imagination the overall sentence means something like: We couldn't possibly learn anything from you, so why should we even have to listen to you?