Thranduil lives in Halls under the mountain, in halls built with the aid of the Dwarves. But do the rest of his people live in the mountain with him, or do they live outside in the wood?
From Legolas' description of the Galadhrim (the tree people) I assume the elves of Mirkwood do not live in the trees like the Galadrim.
This question has been inspired by a discussion about a piece of fan art posted to a facebook group that purports to show the Mirkwoodian elves.
I think it looks like a generic fantasy image, rather than of Mirkwood elves, but then I realised that I don't know how they actually live.