Hmm... on non-native English speakers grappling with English... well, my family (the ones who are 1 or 1.5 generation American immigrants) are a mixed lot. Most of my grandparents have relatively good English.
All of my grandparents came from well-to-do families, i.e. the scholar-gentry class typical of the Sinosphere, and because of this they all had a relatively easy opportunity to learn English/French and be forced to interact with people who knew English/French (whether it was due to their job, or for reasons of prestige/"ooh look I'm sophisticated and high class"). My maternal grandmother, for instance, went to college in the US and was the principal of an international English school in Vietnam, and as such the ability to communicate in English was very important. My paternal grandfather, meanwhile, was the spokesperson for first the foreign ministry of S. Vietnam (or whatever it was called) and later S. Vietnam's ambassador to Japan; in such a job, where he would've invariably interacted with English-speaking diplomats and other such folks, the ability to maintain a good level of English fluency was required.
Ultimately, due to this, all my grandparents have a good working level of English even before they came as refugees to America. My paternal grandfather and maternal grandmother in particular; while their English wasn't "perfect", they have little trace of an accent. In a sense they are sort of like one of those people who are fluent in English, yet you can tell they aren't native/didn't speak it form a young age. Thus my grandparents have been more or less able to handle communication in America much more easily than other immigrants - not only did they know the language, they knew how to use it (for instance it's one thing to know how to talk, but it's another to be able to, say, negotiate the price of a car or understand which politician suits your ideolkogy better). However, because they spent much of their adult lives in Vietnam, and here in America many of their friends and family are Vietnamese, their knowledge of Vietnamese is pretty much intact.
As for my parents and uncles/aunts, since they 1) were already exposed to English from an early age due to the social status of my family in Vietnam before we fled; and 2) came to the US at a very young age (my youngest uncle was in fact 6 when he came here), their English is for the most part almost flawless, as befits most 1.5 generation immigrants anyways. There is still the faintest hint of an accent, but you can't really tell that it's foreign unless you listen ridiculously closely. However, it does vary from uncle to aunt and parent. My second oldest uncle, for instance, came to America in his late teens, in contrast to my father who came in his early teens. For this reason, my uncle's English is always so stilted and formal compared to my father's - it's not just a matter of personality (which is true), but also because my uncle came when he was older, so he didn't have as much time to, say, go to school and get accustomed to the language the way my dad did.
Conversely, when it comes to Vietnamese, oddly my parents and most of my aunts/uncles have a level of competency equal to that of my grandparents while still maintaining fluency in English, which is slightly unusual for 1.5 generation immigrants, who either do well in one or another depending on their circumstances. This seems to be due to their background, too; coming from a traditional, scholar-gentry family, even if they weren't forced to learn literary material, say, they naturally had an inclination to study it either out of a sense of obligation or just for personal pleasure.
As for me and my brother, and our generation, we are much better in English, but we are okay at Vietnamese too, compared to other second generation Vietnamese, some of whom don't understand a word of it at all. The reasons are: 1) we went to Vietnamese language school on the weekends when we were young, which forced us basically to constantly review the language; 2) we spoke mostly Vietnamese at home growing up (amazingly we accepted it even though we could've in theory only spoken ENglish to our parents and grandparents and nobody would misunderstand anybody; though nowadays oddly for some reason my dad speaks more English with me than Vietnamese). Granted, its "American" accented Vietnamese, and its pretty messy, but it does the job.
Ultimately my whole point here is this: language competency depends a lot on your personal situation, your personal ability, and a whole variety of factors. Immersion, and immersion in the right place, is important. If I didn't speak and hear a lot of Vietnamese, I wouldn't know anything. If both sides of my family didn't have a literary, "high-class" background, I wouldn't have knowledge about random aspects of more formal, literary Vietnamse. If my grandfather didn't have to deal with English-speaking diplomats all the time, he wouldn't have known how to carry a pleasurable conversation with random people in America. If my dad didn't hang out with all those black kids in the first American high school he went to, he wouldn't have been able to pick up on the (now outdated) African-American slang he can use to communicate with African-Americans his age.
Stuff like that.
Also, as a side note, since my grandfather was under the ambassador to Japan for a few years, my father and hs siblings also lived there. THough they went to an English international school, they did pick up quite a bit of Japanese (language-wise and culture-wise). My father apparently was semi-fluent by the time he had to leave, though he has forgotten most of it. However, if he were to study Japanese again I think he'll pick it up in no time. Additionally, since he lived in Japan at that tender, pre-teen/early teen age, when you learn your first curse words, when my dad gets pissed the first curse words that come to mind are Japanese (so he's told me). Anyhow, if you're young and more susceptible to influences, it can be easier to pick up languages.
