I would personally think that, if they're using magic to get around the language barrier, it works perfectly. Their grammar is impeccable, probably more strictly correct than that of the native English-speakers they're talking to. Having major and supposedly intelligent characters communicate in poor English throughout the book is just a needless annoyance for the reader, unless you do it masterfully (which almost nobody has ever done). They probably speak in a very precise but slightly stilted way, a lot like anybody from a Jane Austen novel who wasn't working-class. Here's how to make them alien. Some things simply don't translate, so every so often, the construction of a sentence is just plain wrong. The example that springs to my mind is a Tim Powers novel I read ages ago, the title of which I forget, in which the hero interacts a lot with elves, humanoids who have a totally non-human mentality which the reader never really gets to grips with. At one point, their leader says to him: "We have decided to like you." See what I mean? That's absolutely perfect in terms of being subtly alien! No human being would ever speak that sentence unless they were a grinning cult weirdo you probably wanted to run away from screaming. But for elves, it's the literal English expression of what they feel. There's no backstory explaining whether they have a telepathic hive-mind, or hold committee meetings to decide everything, or maybe have insanely detailed rules governing social interactions written down in million-year-old books. Maybe all or none of the above. Who knows? They're just being elves.
I'm glad you're not going with the broken English approach. Not everyone who doesn't speak English sounds like a caveman. Unless you're speaking a language you are very proficient at, you don't just "pick and choose" the most obvious words. You think of what you want to say and then you translate it, usually as accurately as possible. Having a lack of articles is one of the least realistic ways of representing a foreign language. As a matter of fact, most eastern European cultures tend to add articles where none should be present, because in their own language that's how they would say it. If in your own language you would say, "pass me THE food" you would never translate it into "pass food" when speaking another language. You would look for those words you would regularly use. And articles are not difficult to learn. A lot of Orientals sound like cavemen only because their original language does not employ articles. But really. So long as you have lips and a tongue, I'd say English is the easiest language to learn. A lot of foreigners consider English to be a sort of universal language, because it's so easy to grasp the basics and because it is so widespread now. I've met people who hate English (simply because they hate the west) but they still use it when traveling internationally because certainly someone will speak it.
They could know English but not know normal human social conventions, what sort of things involve tact and what don't, and that sort of thing. So instead of: "Good morning, Joe. Thank you for arriving so promptly." They might say, "You are early. This is inconvenient. Go out and return at eight o'clock. First, why are your shoes always dirty when your companions' always look clean?" No "please", no pretense that it's helpful to arrive before your hosts are ready, no realization that comments on personal appearance are a problem.
Wouldn't the OP first need to know if their original language employs articles? If he was to go down the articles-all-over-the-place route, which is something I've seen my fair share with both speakers of languages that employ articles (like Swedish speakers) and with speakers who don't use them (Finnish), he might want to first decide what the mothertongue of the representatives of a given race is like. A lot also depends on the individual. I had a French penpal who was terrible with articles and prepositions, even though French employs them both in a somewhat similar fashion (in comparison to languages like my mother-tongue which is agglutinative). The key to communication is the range of vocabulary, methinks. You play with nouns and verbs. There's more leeway with articles, pronouns, and prepositions, and for certain speakers they're quite easy to get wrong. As long as their original language doesn't work like those languages that rely on context instead of determiners. Anyway, this is probably a moot post if they've learned English magically, so unless there's a glitch in the magic, they'd speak it perfectly.
