Here's a list of all the languages, including keys used to talk in them and a brief explaination of what to expect when you hear someone speaking in it over Common.
Siik'Tajr - :j - Often used to discuss home life or plans on-board the station. Tajarans speak this.
Canilunzt - :7 - Always used to discuss drama on-board the station between other Vulpkanin and/or crewmembers in general. The infamous Vulpkanin speak this.
Sinta'Unathi - - Used to complain about their personal lives, or how few Unathi there actually are on-station nowadays.
Skrellian - :k - You will never fucking hear this. There are never enough Skrell players on one shift to justify them using their own language.
Rootspeak - :q - Used between Diona as a way to express their disgust at the world around them, and also to bitch about how slow they are.
Chittin - :4 - "Are there any other Kidan on-board?"
Vox Pidgin - :v - Always used to discuss nefarious deeds or to shit-talk dustlungs. Get the AI to translate it ASAP. You never know what they might be up to.
Bubblish - :f - Slimes use their own language to discuss what flavour they are. That's literally it. Don't even worry about it. If the AI translates it, chances are it comes up as nonsense.
Psionic Communication - :^ - You will never hear this over common, nor will you hear it in person, because it isn't a spoken language. If there's a group of Grey sitting around in total silence (unlikely), be very afraid.
Trinary - :5 - Walk around with EMP grenades or the ion rifle just to strike fear into the hearts of the IPC crewmembers, because Trinary is almost always used to talk about some form of Synthetic Revolution.
Orluum - :% - You'll never hear this, because Drask died out about as quickly as they arrived.