Real answer: these are actually real languages! They're just conlangs, or constructed languages, instead of natural languages. The major problem with conlangs generally ends up being the limited vocabulary, but the grammar foundations are usually solid.
I actually really like Klingon as a language because it was intentionally designed to be alien, and specifically to be very Klingon. Most languages are Subject-Verb-Object (like English and other Western languages) or Subject-Object-Verb (like Japanese or Hindi). Klingon, however, is Object-Verb-Subject - it's very direct with the emphasis placed on the target of the sentence, which makes sense with the Star Trek world and Klingon culture.
Fun fact, Klingon has at least one native speaker - some guy raised his daughter to speak Klingon as well as English. (I'm not a fan of this - on one hand, learning multiple languages from an early age is a huge leg up in being able to learn more languages in the future, but on the other hand Klingon is entirely useless as a primary language given its structure and the few other people who speak it.)