To which extent is just interchangeable with simply, as in the example?
It's becoming more than just annoying.
It's becoming more than simply annoying.
Is just synonym of simply in just any case or are there situations where the two adverbs convey slightly different meanings?
Also, Google gives 1,800,000,000 results for just and only 295,000,000 results for simply. Is one preferred over the other?
Just and simply have some overlapping meanings, but definitely do not overlap in all meanings. In your example, it is a case where they have essentially the same meaning.
However, just (the adverb) can also mean "only now". For example:
How long have you been here? — I just got here. (=I arrived right now.)
Simply cannot be used in this instance.
(Note: I assume that we are only talking about just as an adverb; just can be used as an adjective too, meaning "right" or "fair". I don't think you are concerned about that one, because it is clearly totally different in usage.)
The second sentence sounds odd and is incorrect. "Just" and "Simply" do not have the same meaning, however, these can be interchanged in most situations; though not in this one.
As adverb, just means:
There are then cases where just can replaced with simply without to change meaning to the sentence.
As examples of usage of just the NOAD reports the following sentences:
That's just what I need.
You're a human being, just like everyone else.
Conditions were just as bad.
I've just seen the local paper.
I got here just after nine.
They were just interested in making money.
There also phrases where you need to use just, as in just about, just as well, just in case, just a minute; replace just with simply, and you get a phrase without sense.
The results obtained from Google don't mean that, as just appears more frequently than simply, just is more preferred. As the words are not synonyms, comparing them is like to compare the number of sentences containing house with the number of sentences containing moon.
With Google, then (as reported by other comments), you don't obtain results for English only, and you can obtain also results for phrases that are not grammatically correct.
"Just" (adverbial), "merely", "only", and "simply" can mean exactly the same thing in certain contexts. However, as kiamlaluno points out, there are at least four distinct meanings of "just" used as an adverb.
In the example "just as well" provided by kiamlaluno, the meaning of "just" is "equally", but it is not being used an adverb.
Dusty misapplies one of the meanings of "simply" ("not complex enough to include additional values") which is irrelevant to the case at hand.
