I always heard the saying as “Chicago is the second biggest Polish city in the world, after Warsaw”. If you count “Chicago Metro Area” as “Chicago”, it is correct, since AFAIR there are approximately 1.5M people who claim being “Polish Americans” in Chicago Metropolitan Area. Only Warsaw (at 1.7M population) is bigger.
Melbourne has the world’s third largest Greek-speaking population after Athens and Thessaloniki.
Well, let’s look at one common claim. “New York City has more Jews than Jerusalem.”
Is this true? Well, the city of Jerusalem has a population of just under 800,000 and the metropolitan area has just over 1 million people. Bear in mind, a large chunk of those people are Arabs, not Jews.
New York City alone has almost 2 million Jews.
So, in this case, the statement is literally true.
I think you mean "Muslim/Christian not Jews, as there are Arab Jews
One thing is for sure. NYC has more Lesbians than the Island of Lesbos does.
It also has more men than the Isle of Man.
Cleveland is my birthplace, and I never heard that one. But I’ve always heard that Cleveland has more Slovenians than anyplace outside of Ljubljana, which I find more credible. No idea how to verify the figures, though. (You’d have to start by subtracting the populations of Austrians, Croats, Italians, etc. from the total for Ljubljana.)
(Edit–But I am pleased to know that the one time Béla Bartók visited Cleveland, a guest of the Hungarian community there, he insisted on going to an African-American jazz club where he sat by the pianist and took notes. Literally note notes.)
This article says that the there are over 50,000 Samoans in Los Angeles. Wikipedia puts the population of American Samoa at a bit over 55,000 as of last year’s census, so the numbers are comparable. There might have been more Samoans in LA in the past, as I’d imagine that at least some Samoans have moved out of LA into other cities.
It’s true about many languages.
There are more English speakers in the United States than there are in England. More Spanish speakers in Mexico than there are in Spain. More Portuguese speakers in Brazil than there are in Portugal. More Arabic speakers in Egypt than there are in Arabia.
It has been a while since I heard that. Back in my Hawaii days.
Back when he was the mayor, Ed Koch (in a Playboy interview) said that New York had “more Irish than Dublin, more Jews than Tel Aviv and more Blacks than Nairobi.” A scaled-back claim, but there you are.
Is this counting the ones that most Americans consider Jewish but you don’t? 
Your wiki gives some conflicting numbers. So does this entry.
Feel free to keep the settlers on your side! 
There are lots of cites for St. Louis having the largest Bosnian population outside of Bosnia. Here’s one: http://www.fontbonne.edu/academics/undergraduate/departments/englishcommunication/bosnia_memory_project/st_louiss_bosnian_community/
With a population of 12 million in Tokyo (and much higher in great Tokyo), you’ll never find a city or even county with more Japanese than this.
I’ve also heard that more recently, there is more Scottish Gaelic spoken in Nova Scotia and PEI than in Scotland itself.
Without looking it up I’m going to say that this is incorrect. Scots Gaelic has largely died out in its former strongholds in NS and there are still 50,000 speakers of Scots Gaelic in the Highlands and islands.
That’s how it usually works with immigrant languages. A language that only people in your neighborhood can understand just isn’t very useful, and within one or two generations it’s largely been forgotten.
Not to mention having its own BBC television channel in Scotland.
I’d love to be able to get this channel.