Great Question!
I'm interested in the answer to this as well, so I hope someone more expert than I will come along and answer it.
But if you'd like my two cents worth, subtle is definitely the way to go. Using funny spelling to indicate dialect and accents is considered very cheesy, according to the masters. So no "Ve haff given you varning!" for the German-speakers. But I think you knew that.
Rhythm and diction are the answer, apparently. That is, the words they choose, their length and the order in which they contruct syntax convey these differences. Easier said than done, I say.
I think it involves a lot of listening. At least that's what works for me, but I've had quite a bit of experience listening to non-anglophones speak English, and so I try to remember how they talk. They typically use simpler words, depending on how fluent their English is, but what constitutes simpler may not be obvious. Many common English words are short, but they're of Anglo-Saxon derivation and irregular, so some people will choose longer latinate words that have cognates in many European languages, or maybe verbs with simple conjugations. Though a German might find those short words familiar.
Also I've noticed that people tend to carry over their own grammar when speaking foreign languages so that they may say things that are technically correct, but are odd choices. Russians, for instance, seem to use lots of progressive tenses. Instead of "We'll get together at five" they might say "At five we are getting together." I think that has something to do with the use of imperfective tenses in Russki yazik.
So my advice would be to listen to people from the nationalities in question enough to get a good feel for each one. Then you'd have to imagine how each character talks in your head, and work on that until you can tell what he or she would say versus what doesn't sound right. You'll probably have to read your dialogue out loud at some point to get this. Hard work! But as you get to know your characters better it should go faster. And just like real people they may sometimes surprise you.
Again, I'll be looking for advice or tricks of the trade from a real pro. But this seems like something different writers handle differently, and when people find ways to do it that work it's impressive. To other writers at least. So you may discover a way that will have us all slapping our foreheads and saying, "Why didn't I think of that?"