[I speak from experience with math journals. As always, if things differ in your neck of the woods, I'd like to know.]
The quality of the writing of an academic paper is one of the two main things that the referee is being asked to evaluate in her determination of the suitability of the submitted paper (the other of course being the content of the paper). In mathematics the quality of the writing and the quality of the content are usually largely separate entities, although I think it is an oversimplification to regard them as totally separate (to write a math paper well requires more mathematical thought than to write it decently, which requires more thought than to write something badly but that a qualified expert can see essentially does accomplish what it sets out to do). I think that this is less true in the humanities, but I'm not fully qualified to say more than this.
The "default" for math journals is that they say that their papers should be sufficiently well written in order to be published: of course this is a nearly useless statement.
I include that vacuity to contrast it with what certain other journals do: namely explain to what extent expository considerations are weighted in with the "content" of the paper in arriving at a decision. For instance some journals say that they welcome "expository" papers. In my experience they rarely mean this; much more often what they actually mean is that it is unusually important to them that the papers be well written, and that a research paper which has fewer results but that is truly attractive in its writing may be worthy of publication. The MAA (Mathematical Association of America) journals take exposition much more seriously: for the Monthly they seem to be about equal; for Mathematics Magazine and College Math Journal, good writing seems to be more important than content. I am tempted to tell a personal story here, but I will save it for a more appropriate time. Well, except for this: I got a referee report back from the American Mathematical Monthly saying "I give this paper an A for the mathematics and a B for the writing." For any non-MAA journal that would have been a strangely worded stamp of approval, but for the Monthly it made me nervous, and I worked hard on yet another revision.
There are also some research journals which have a reputation for accepting sloppily written, but contentfully deep, papers. The one which stands out in my mind is the Asian Journal of Mathematics. It sounds bad, but in my field I get the impression that if you have proved a great result and for whatever reason can't indulge in the luxury of writing it up properly -- by properly here I mean "formally completely and correctly", not "well"! -- then AJM is the journal for you. And it sounds worse than it is: if I'm right then it's good to have journals like that, and in some ways of course they are better than the journals which publish perfectly polished, but very minor, work.
Anyway, back to your question. What to do if the writing is bad? The answer is that you should indeed report on this and try to discount the value of the paper appropriately (neither too much nor too little), according to your best understanding of the demands of the journal (or conference?). It seems quite reasonable to me to write back to the editor asking whether the journal (or the editorial group) has definite opinions on the desired writing standards. Working off the cuff, it seems reasonable to identify three levels of bad writing:
1) The prose is not pleasing, the writing doesn't flow, and so forth. In other words, the style is bad, up to the point where the paper becomes less pleasant to read but no farther.
I think that for many journals and conferences this would be a minor offense. Especially, if you are participating in an international academic scene, then really the authors are doing the academic world a great service by writing in a language that the vast majority of the contemporary academic world has learned to read. You speak particularly of Asian authors. Well, it is rather gracious of them not to write in, say, Chinese, isn't it? For this level of bad writing I think it is best to mention it but make clear that it doesn't really detract from the paper. It would be nice to offer to help out in the editing, if you want to, but it is not clear that it's your job.
2) The writing is bad enough so that it interferes with the meaning, and an expert has to work harder to read it than she would for a decently written paper.
This seems to be what you are describing. Here I think I would really ask for guidance from the editors of the journal: the worth of the paper should be downgraded for this, but by how much? A paper which one has to struggle to read but ultimately succeeds in doing something brilliant or ground-breaking is still a great paper. (And in my field, very few brilliant or ground-breaking papers are really "easy to read". At a certain point you get past the writing altogether...provided the writing lets you!)
3) The writing is so bad that a qualified expert is unsure of the meaning, either at multiple lesser points or at at least one key point.
In this case you can't certify that the content is legitimate, so you have to recommend the paper for rejection, right? You should indicate exactly why you are rejecting the paper; in many situations, a paper which is rejected for bad writing (but not obviously defective content) may only then get the attention to writing that it actually needs and then come back as an acceptable paper. When I reject a paper for bad writing (which rarely happens, but it has happened) and I suspect that the content is also not sufficient, I try to at least hint at that in the report...otherwise the danger is that everyone's time (including yours!) will be wasted by a revision which is more superficially acceptable but still defective on a deeper level.