The thing is, most "Austrians" traditionally avoid conventional mathematical models, as well as formal notations, preferring to use plain textual reasoning. In some aspects it's good: they do not limit themselves only to what is easily rendered to math (correlations go well with maths, causal relations not so well (but perhaps manageable), formalizing teleological reasoning about human choice-making is much harder).
In other aspects, the lack of formal notations is really bad: most modern economists have mathematical, not philosophical training, and to an unaccustomed eye the Austrian texts actually do look like non-sensical hand-waving. It takes quite some studying to see the actual rigorous structure and careful choice of terms behind those walls of text -- and I won't go into why there aren't that many incentives for most people to study those kinds of books.
I actually think Austrians would gain a lot from adopting more formal notations (perhaps not of the kind adopted by mainstream nowadays). After all, Hayek himself have failed to finish his own book on the theory of capital (which is one of the distinctive concepts in the Austrian economics), because of the sheer complexity of it. Keeping rigor and precision without the formal language is really hard; and formalized representations might be better suited for independent review and verification.
However, in case of economics, the problem domain doesn't lend itself for easy formalization.
> Does Austrian economics make an testable predictions? Is it based on empirical data?
These are some hard questions about Austrians that pop up quite often. It's true that at its heart much of Austrian economics is based on deductive reasoning from a priori assumptions (the correct analogy, they say, is mathematics, not physics). Theories do not follow from the facts; instead, the observed facts are explained on the basis of the theories we find reasonable, and the best theories are those that provide the best (i.e., the simplest and the most general) explanations. This is not really a uniquely Austrian approach, but I believe it's a good way to approach their research.
However, there's not a single strong view on apriorism even within the Austrian school. Mises indeed was quite a radical a-prioist. Hayek and Menger much less so -- and that, I believe, for a good reason.