Birds = Nest. Usually romantic connotation. e.g. 'Love nest' Den = Dragons! Also often connected with thieves, prostitutes, drug addicts and other fun to be with people. Lair - any wild animal shelter. again, negative connotation.

Den and lair are synonyms as far as im concerned. A nest is where birds live and keep their eggs. You may hear such expressions as "A nest of criminals" in literature.