Note 1: as per your previous post, put these messages in the Processing with Other Languages section, please.
Note 2: "why then you do not write it in the reference?" You should address such question to the Processing.js community. It is distinct (but indeed strongly tied) of the Java Processing community / developers.
Note 3: I believe most of the PJS reference is just a verbatim copy of the Processing reference, lacking to address some limitations or specificities, indeed.
Note 4: you can send a short message to the server by using loadStrings("http://yourserver.com/stuff/save.php?data=some+data+to+save") for example (making effectively a GET request). I don't know enough PJS to say if there is a better way.

You should have a look at that:
https://groups.google.com/group/processingjs/browse_thread/thread/585611186fb1deca?pli=1

Thanks for commenting, Makio135 (I was hoping you wrote...).
The point remains, that the specificities of saveStrings() and similar should be documented on the PJS site.
I see in the thread that it now uses local storage, which might fail on some browsers, this can be worth reporting too.

Side note: I don't know how local storage is really implemented. Does it results in a real file somewhere, that can be copied / opened in text editor or something else (yes, that's a lazy request, as I can google too, but still that's a useful information to give in this thread).

Last note: beside the Ajax request shown in the thread, I suppose one can use JavaScript to build a form (perhaps in an iframe) and to submit in GET or POST mode. All things not obvious for a beginner knowing only the Processing syntax.

Without testing your PHP code, I think it should be:
loadStrings("http://alumni.vgtusa.lt/test/saveFile.php?dataToFile="+testData);
ie. the URL parameter must be the same than in the $_GET[] part.
Note also that testData must not have special chars, like spaces, &, =, etc., or they must be encoded.

The data won't be visible (I think) since the URL and its call is built inside the sketch: the browser won't display it.
You cannot use Java libraries as shown in the wiki article you point out. You can use JavaScript-specific code, like shown by Makio135, although I haven't used PJS enough to tell how to call JS from PJS.

Back! (was reallly busy...)