To be clear there was no nation of Styria at this time (or any time, really). However, Styria was a "country" or "state" in the same way that Moravia, Bohemia (proper), Upper and Lower Austria, etc. were all states within the Habsburg Monarchy. In fact most of the "countries" in EU should have the same structure as the Habsburg Monarchy, that is: they should consist of different states united loosely by a personal union. For exmaple: Spain!
All the states within the Habsburg Monarchy had their own political traditions, some degree of self-administration and parliaments (estates/Stände/cortes) - which of course were not parliaments in the modern sense, as they were dominated by the big landholders in the respective state, or, in the second half of EUs timeline, by the monarch/crown ("absolutism" --> then the nobles had other means of influence, at court). So basically, Styria was just one of many, many states that are not represented in EU at all. EU fails to grasp the very basic political structures and the big development of the age it is set in, I'm afraid. It should be a game of conflict between crown/centre and estates/peripheries. Conflicts of centralization were just as characteristic for the period as conflicts between souvereigns (think Huguenot Wars, think the "Rebellion" of the bohemian estates 1618, etc). If at all, they are represented in EU not dynamically but in scripted and rather supferficial manner. The "countries" that players control in EU are by far too much centralized and unified. An early modern 17th century composite monarchy was very different from a modern nation state!
The whole age could have been represented much more plausibly with the CKII engine (featuring characters and titles) and some tweaks (focus on the political rather than the personal/private aspects of relationships, parliaments as strong "actors"). This way, we could also have courts play their proper role and also favouritism (this was the golden age of grey eminences and favourites!). It would not only give us a much more plausible historical setting/structure, but also the much needed baroque flavour that EU totally lacks.
As it has already been mentioned in this thread, Styria might be included as a souvereign "country" somehow because in 1564 Ferdinands I' heritage (the titles) was split up under his three sons, according to the inheritence law/tradition of the house of Habsburg (later on they finally realized it was not a very smart thing to do...). This led to three well .. semi- or - in InnerAustrias case fully souvereign territories, the last of which were united under one person only under Leopold I. 1655 (?). Archduke (=prince) Charles (the youngest son) received Inner Austria, which comprised the states Styria, Carinthia, Carniola, Gorizia, Gradiska, Trieste, Istria and Friuli. Maximilan, the oldest son, received the imperial crown, the kingdom of Bohemia (consisting of the "states" Moravia, Silesia, Bohemia proper, the two Lusatias), the kingdom (you might also call it empire) of Hungary and the two Austrias (Lower and Upper Austria). Archduke Ferdinand, the middle son, received Tyrol and the "Vorderlande", that is a lot of tiny territories in what is today southern Germany.
As for sources for Styria: you could just look up any good history of Austria. The one standard reference for the Habsburg Monarchy in this age are the two volumes by Thomas Winkelbauer, Ständefreiheit und Fürstenmacht 1522-1699. Of course there might also be articles in history journals on the estates of Styria in particular (Styria was also very involved in organizing/paying for the habsburg military border). In English, I think R. J.W. Evans, The Making of the Habsburg Monarchy is the way to go and gives a nice overview. I don't know what kind of "primary sources" you'd like to see for Styria.

There are probably millions of documents that have been produced by or refer to the institution of the Styrian state in this age (the estates usually came into being in the late middle ages, when - in absence of "stable" territorial lords - they took over the administration of the country). Perhaps one could find a list of the most important noblemen of the styrian estates (...). Today, Styria is still a federal state of Austria.