I think (a) is the most common. If you say "the glasses" then you're putting special attention on those glasses. Maybe if someone wearing very strange glasses was seen by you then you would say "the glasses" because the glasses are as much a focus of your attention as the man is. When saying "man with glasses" the glasses are treated as a descriptive detail of the man, but when you say "man with the glasses" then the glasses are being treated as a separate object.
Using the word "on" is probably not necessary here. It seems to imply the action of the glasses being put on because it calls special attention to the idea that the glasses are on and not off. A situation where you could use (b) would be if everyone in a group was expected to not wear glasses, but one person was, then you might ask "who is that man with glasses on?"