There is no difference in meaning between any of these constructions. Indeed, you might add two more, which mean the same thing:
Are you going to be using ...?
Are you going to use ... ?
There is no reason to select one over another (but in context whatever forms were used immediately before the question might affect the choice).
With respect to modality, these are all about as mode-neutral as any question about the future can be. None of these questions addresses the interlocutor's "intention" or "will": all of them treat the room's status for tomorrow simply as a determined fact known to the interlocutor.
The interlocutor's intention would probably only come into play if that intention stood in contrast to some other fact; in this case the speaker would probably employ different verbs in her question, depending on the exact situation:
Are you planning/Do you plan to use ...? OR
Are you intending/Do you intend to use ...? OR
Have you decided to use ...? OR
Do you want/need to use this room tomorrow? —because I don't think it's been booked yet.
(These are of course examples which don't exhaust the possibilities.)