In the new movie, Blade Runner 2049, there are several advertisements in Russian, including one that mentions the CCCP (the USSR). Do we know what the current government of LA is? It it under Soviet control? What other languages are spoken, besides Russian, Chinese, and English?
It's in part to do with the fact that there are only a few Megalopolis' left and that Phillip K Dick intended Russia to be a major power in the future.
The only piece of information I can find on this topic for now is that the Director, Denis Villeneuve, has recently stated in a recent interview with Josh Rottenberg (Los Angeles Times):
Part of L.A. is in ruins and doesn’t have power anymore, and there are a lot of refugees coming from eastern Asia and Russia
-Los Angeles Times, 2017-09-01, Denis Villeneuve explains how 'Blade Runner 2049' is no replicant of the original neo-noir sci-fi fan favorite, by Josh Rottenberg
Basically, the world is either too spoiled to live in or has lost its desirability in comparison with the unseen 'Off World' locations. Given that, many people have migrated to the remaining Megalopolis' left, one if which being Los Angeles.
In this world, there’re no more countries, only a few megapolises — Los Angeles, maybe New York, maybe London, maybe Ouagadougou...
The other thing is that in the original novel, Do Androids Dream of Electric Sheep? - which the Blade Runner series is loosely based off, the author, Phillip K. Dick originally intended Russia to have overtaken as a major power or influence in the world, as director Denis Villeneuve stated in a recent interview with Nash Jenkins (Time):
Nash: How do you update a vision of the future from 35 years ago?
Denis: I went back to all the cultural references of the first movie and imagined how they would evolve in the future. And then I went back to the Philip K. Dick novel and explored the geopolitics of the book. In the book, the U.S.S.R. was still present. I thought that it would be interesting to think — what if the U.S.S.R was still alive? What if it was as strong a cultural and economic force as the U.S., but with different political laws? You see McDonald’s in Moscow. What if you saw Russian products in the streets of Los Angeles? I thought that would create an interesting distorted reality that would tell my audience right from the start that they’re in a different world with different laws from a geopolitical point of view.
-Time, 2017-10-03, 'Director Denis Villeneuve Proved to Us He Loves Blade Runner More Than Anybody', by Nash Jenkins
Although the main writers Blade Runner and Blade Runner 2049, Hampton Fancher and David Green have mentioned that the story is not all that related, it's still conceivable that this feature of the world is hungover from Dick's story:
Scott Huver: How much of an influence was Philip K. Dick in the process?
Green: I hope I won’t disappoint to many by saying very little. There are a lot of science fiction writers I love. I have a hard time accessing Do Androids Dream [of Electric Sheep?] specifically, and some of his other novels as well. I think the prose is beautiful, the ideas are amazing, but it’s one of those things that I always read intellectually instead of being able to experience emotionally.
Fancher: Well it was one idea. I was looking for a vehicle, and it was rather cold-blooded on my part. Because that’s what I’d been lacking in everything I’d been trying. I didn’t have through lines. I didn’t have McGuffins. I didn’t have plots, and I was Antonini all the way. It was like, “That’s my way into wherever the gold is.” It was that one thing, and that’s all, and the idea that science fiction was going to become popular in the near future. And so I didn’t have any love of Dick at all. I was never a fan.
This is why there are a lot of visual indications of the USSR being present in the world, but not a lot of story to go with it
It's safe to assume that the government is not under Soviet control as we see no evidence thereof. However, I'd urge you to ask yourself: "In that world where everyone lives in the same place, homogeneously, how do you define 'Soviet'?"
Again, there's not much evidence towards which languages are spoken, officially. We see a few examples though:
Morton's greenhouses all have a Russian word transcribed on them - 'Целина' ('Tselina') which roughly translates as 'virgin soil'. This word used to have a deep cultural meaning in the USSR: throughout the existence of the country, there were big waves to develop uncultivated lands in different corners of the Soviet Union.
Also the old lady is definitely not speaking Russian, but also not sure if that was Chinese. I was thinking Hungarian, maybe?