Disclaimer: I'm part of the MathJax team. Also, this got a bit long.
tl;dr Try out NVDA with MathPlayer 4 on Firefox here on math.SE
JAWS 13 is a bit old (2011) and the situation of screenreaders with respect to math and the web has changed drastically since then. As already mentioned, JAWS 16 was the first version to introduce direct MathML support but as far as I know earlier JAWS versions played well with MathPlayer 3 on IE<10. For the longest time, MathPlayer was the only solution for rendering MathML accessibly on the web though it only worked on IE. With IE10 deprecating plugins like MathPlayer 3, MathPlayer 4 is now more of a third-party library. As far as I know, MathPlayer 4 drives most screenreaders claiming math support. Notable exceptions are Apple VoiceOver and Google ChromeVox. While neither matches MathPlayer's output quality, VoiceOver comes built into all Apple products and ChromeVox is both a Chrome extension and built into Chrome OS and Android Talkback (it is also open source which is great).
MathJax converts its input into MathML internally and then converts that to HTML or SVG so that it renders well visually. This is a problem for accessibility since MathML itself cannot be used, so even those screenreaders that support (some) MathML won't see it (well, actually, ChromeVox and Texthelp hook into MathJax to get the MathML and match it with MathJax's visual output but that's only possible because they work in the browser directly).
To improve the situation, we developed a new extension (AssitiveMML.js) as part of the MathJax v2.6 release. This is currently in beta testing here on math.SE. The extension embeds MathML alongside the visual rendering hiding the visual rendering from AT and the MathML from being visible. That's clearly not ideal - in fact, usually bad practice - but it's the pragmatic solution we followed after feedback from AT vendors and accessibility experts.
For more information on the extension and the kind of screenreader support you can expect see our documentation. For Firefox, both JAWS 16 and NVDA+MathPlayer 4 worked well in our tests.
In case you prefer reading TeX source directly (which some AT users do), then you could use one of the scripts from the community here to prevent MathJax rendering.
For what it's worth, we (MathJax) are also working on a stand-alone, on-the-fly accessibility solution that is designed to work with all screenreaders supporting ARIA live regions. I think JAWS 13 supports them though it might not be compatible with recent browser versions; I'll try to find the time to add it to our tests.