There's obviously gonna be different explanations for different characters, but here's my two cents, in the form of two ideas (and indeed it could be any combination therein).
1.) Immortals such as the Elder Gods, Titans, Raiden, and Fujin may have simply picked up these languages due to their long lives, such as Raiden being exposed to pretty much all of Earthrealm's languages over his long tenure as protector. He would also, naturally, pick up on the languages of other realms variously based on further exposure (for instance, we know he's been battling Outworld for at least 500 years (though likely much longer than that really)).
Shang Tsung is obviously native to Earthrealm, but he's also known for his habit of taking people's souls. In doing so, not only would he be able to take their forms and recreate their abilities--even expanding this to those he doesn't absorb--he'd also be learning any sort of languages they know. And combine that with his unnaturally-extended lifespan due to aforementioned soul-napping, and he'd have the ability to learn every language in Earthrealm and beyond.
The long lifespan explanation also extends to a lot of other characters, such as Shao Kahn (who may or may not be a god himself) who has been trying to conquer Earthrealm for centuries, Kitana and Jade who are 10,000 years old due to Edenians being naturally long-lived, Goro who has been fighting in Earthrealm for 500 years so of course he'd learn Earthrealm languages, Geras who has traveled Earthrealm for literal millennia, and Bo' Rai Cho who probably learned English due to living in Earthrealm, etc.
Quan-Chi is a demon from hell, so he would have had heavy exposure to a variety of different languages from throughout the realms.
As for characters who aren't long-lived, such as the Earthrealmer characters, many of them are likely using English simply as a Lingua Franca to converse and coordinate, especially given the fact that English is the most widely spoken language on Earth (While Mandarian has the most speakers on the planet, English is more spread out while also having a large native speaker base). Remember that characters like Scorpion aren't ancient warriors, but rather are modeern warriors. The Lin Kuei likely teach many of their warriors English for their missions.
2.) Indeed, due to the Mortal Kombat tournaments, as well as how central Earthrealm apparently is in the cosmology of the realms, English may have also spread to the other realms like Orderrealm and Chaosrealm through cultural osmosis. This would also likely mean that before English, other languages may have played the role of lingua franca, such as Edenian long before any Earthrealm language took up the role (since Edenia was conquered 10,000 years ago), (all the languages presented from here on are purely conjectural) and then would be followed by Outworlder languages, and then a variety of Earthrealm languages, such as possibly semitic languages (such as Akkadian and Coptic), which would then be followed by either an ancient Indian language, then an ancient Sino-Tibetan language, then probably alternated between Tibetan, Chinese, and Indian languages, and then with the rise of the British Empire, English would start to take that role, and then here we are.
As for characters talking in contexts where it wouldn't make sense for them to be speaking English, such as when Shao Kahn and his followers are doing all their scheming in MK 2011, it's simply for the audience's convenience. In historical-fiction movies taking place in non-English speaking countries, we just assume they're speaking some other language for instance, and in sci-fi and fantasy fiction it's much the same. And really, this just sort of applies to the real world explanation as a whole. The rest of what I said above is really just me thinking aloud so to speak.
