###Houses or huts on the ground and in the branches
Houses or huts on the ground and in the branches
In fact the subjects of the king mostly lived and hunted in the open woods, and had houses or huts on the ground and in the branches. The beeches were their favourite trees. The king's cave was his palace, and the strong place of his treasure, and the fortress of his people against their enemies.
The Hobbit, Chapter 9, Barrels out of Bond
The majority of Thranduil's people lived in such buildings. The minority;
In a great cave some miles within the edge of Mirkwood on its eastern side there lived at this time their greatest king. [...] This great cave, from which countless smaller ones opened out on every side, wound far underground and had many passages and wide halls; [...].
The Hobbit, Chapter 9, Barrels out of Bond
Certainly, the Halls of Thranduil were quite big, and it's very likely that the minority of the Mirkwood elves lived in the palace itself.
So, they either lived in Thranduil's halls or in houses/huts within Thranduil's boundaries.