What conlangers do is called, unsurprisingly, conlanging. They study linguistics, especially typology, on the lookout for weird features to build into their langs, and their stories and games, to help generate that essential "Sense of Wonder". The entire movement is heavily influenced by Whorfian memes, which often makes for interesting stories.
I learned these facts, and many others, while attending F/SF conventions and giving talks there about how lame most of the "languages" that appear in fantasy and science fiction are, by comparison with the true weirdness of real human natural language. Eventually I put up a couple of web pages about my adventures at NorWesCon, a convention that takes place annually in Seattle on Easter weekend:
There are a lot of resources available for conlanging; one that I can recommend especially is Mark Rosenfelder's