İngilizce çevirisi

V1l3 duds=dudes? dudes can also be duds or wear them...lol
That's ok - messed up big this morning - can't remember the song...
--
They drive to a strip mall in a glamours limos. -- glam or glamorous; glamour is something else

Москва не хуже Нью-Йорка. А песня мне не нравится совсем :(

I have no idea about the song's content or how close the translation is to the original, I'm assuming you got that right. Just a few things to make it a little more clean in English:

But, dudes, I have tell you, nowhere HAVE I seen
THE Bourgeois AS OSTENTATIOUSLY fat AS they are in Moscow. (x2)

They CHOW DOWN ON bowls of caviar for breakfast.
They drive to a strip mall in () GLAMOROUS limos. > no "a" before "glamorous"

They withdraw money in rubles, dollars and hrivnas. (I have no idea what a "hryvna" is, so I'm leaving it alone, but is it a typo?)
They eat lobsters while laying on the white SABLE FURS,
("laying" is fine, and is what most people would say, but it's grammatically wrong, it should be "while lying on...". But, it's perfectly fine to say "laying". I wouldn't, but I sound like a professor. For such a song, it's probably best to use the coloquial "laying" just like you did.)
And into () golden toilets they poop and vomit (x2) > no "the" before "golden toilets"

There, chicks ONLY TAKE TAXIS to work,
Moscow is an eyesore to () Mother Russia, > no "the" in front of "Mother Russia"

The entire country is like HOME IMPROVEMENT.
SPENDING ALMOST THEIR ENTIRE PAYCHECKS
FOR RENT ON SOME low-income (BR: "FLAT", AM: "APARTMENT") in A shitty hood. (x2)

STREET SWEEPERS RUN AROUND SHAMPOOING THE CITY,
THE CITY LIGHTS SHINE UPON IT for no reason,
But in our town there ARE no STREET LIGHTS
And THE roads are muddy, just like our souls. (x2)

THE CITY disappears, vanishes, evaporates... > (You have to say "city" again, or your talking about the last thing mentioned, which is NOT Moscow, so it's confusing if you don't bring Moscow back into the sentence here.)

But I know, the day will come, WHEN THESE dreams will come true
And we will come to Moscow and enter THE Kremlin on our trucks.
WE'LL start an orgy to praise ALL OF US WHO AREN'T FROM THERE
And we will POUND the HELL out of ITS big bells.(x2)

But as of now, I used my RAINY-DAY savings
to buy the cheapest train ticket to the Capital. (I normally capitalize "the Capitol" unless there's something following it "the capital of the Russian Federation." This grammar rule has changed, so you don't have to capitalize it. But you're using it a replace a city like Moscow, and Moscow is capitalized so "the Capital" should be too, IMHO.)
I am going to conquer Moscow FROM THE KIEV TERMINAL
Dear big city, "HEEEEEERE'S JOHNNY!!!!" Open your arms! (x2) ("Heeeeere's Johnny" sounds great here, like the murderer from a famous Steven King's horror movie called "The Shining". )

Ha ha, we have the same at home. Our Minister of Ecology has just been fired because of his (and his wife's) costly tastes, using public money. Everybody in France is making fun of the giant lobsters he used to serve to his guests, and of his hair dryer decorated with gold leaf. But Wikipedia doesn't say a word about the lobsters, there is a special committee there, preserving the good reputation of people in public life I think.