Is it very difficult for international applicants to get a Visiting Assistant Professor position in the US? I am a mathematics postdoc working outside the US and this year I am preparing for applications for positions (mainly in the US). I should also add that I am not a US citizen.

Sometime ago I have seen in the comments to a question here somebody said that tenure track positions are unlikely (though not impossible) to be offered for people working outside USA. I can understand this, since a tenure track position is meant to end in tenure, I mean, I have the impression that universities hire someone with the intention/hope that he/she will be granted tenure eventually.

I am hoping to secure a 2-3 years visiting position in mathematics so that I can introduce myself to the academia in the US, and then maybe apply for tenure track positions. But the question is, whether the same thing is true for these positions. That is, is it hard to get even a visiting position for someone working outside the US?

Also, I have a good command of English and a high TOEFL score. Do you think I should add this to my application package (e.g. mention it in the cover letter, or attach a copy of the test result, or have it sent to the universities etc.) to counter the fact that I am not a native speaker of English?
I'll mention a few important issues here:


There are relatively few visiting positions in mathematics with a certain term of more than one year.  Rather, most of these positions have a term of one year, and may be continued for another year or two if the need for the visiting position continues.  Visiting positions like this are typically created to fill the hole left by a faculty member on sabbatical leave or as a temporary replacement for a faculty member who has resigned, retired, or is too ill to work.  Generally, the plan is to get a tenure track faculty member hired during the one year term of the visiting position.  There are certainly some circumstances in which a visiting position is setup to last more than one year, but these are very desirable positions and the competition for them is intense.  Thus your chances of finding a visiting position with a term of more than one year are limited.  
In order to work in the United States in a visiting position, you will need to have an appropriate visa and the types of visa that are appropriate here (most likely a J1 visa for a temporary position, but perhaps an H-1B visa) require employer sponsorship.  Your potential employer must pay fees to apply for such a visa and typically will need to retain a lawyer to assist in the process.  This can cost thousands of dollars.  Furthermore, there's a substantial risk that the visa might not be granted or might be delayed.  Because of these issues many academic departments are hesitant to hire applicants who must be sponsored for a visa.  In my experience, many universities and academic departments will undertake to sponsor newly hired tenure track faculty but don't want to do this for a visiting position.  
Most visiting positions in the US are focused primarily on teaching.  The hiring committee will be concerned if you have not had experience teaching in the United States, because there are substantial and important cultural differences between the US system and higher education in other parts of the world.  The hiring committee will also be concerned if English is not your native language.  
There will almost certainly be many (tens if not hundreds) of well qualified US citizens and permanent residents with appropriate teaching experience in the US who will apply for the position.   


If you have a strong record of research and would otherwise be qualified for a tenure track position, then you might have a better chance of getting hired into a tenure track position than into a visiting position.