Historically, Poland stayed the heck away from the war in Germany. They didn't really have any reason to get involved anyway, if only because military adventurism wasn't a big hit amongst the ruling class (who were doing pretty well as was, and busy dividing Ukraine) and the drawn-out mess didn't exactly offer very good expense-profit projections. And I don't think there was any love lost between the Habsburgs and the Polish Vasas either; the Poles had a long history of seeing off German expansionism...
As far as religious divides go, keep in mind that the patently Catholic French monarchs were only too happy to help Protestants, or for that matter anyone else, against their old (and also patently Catholic) Habsburg arch-fiends... although they spent most of the war providing financial support; when they finally joined in openly they had some catching-up to do in military matters (not having fought a major war in quite a while, and hence a tad behind the times), but were soon able to pretty much knock Spain out of the equation and cause considerable problems to Imperial regions in Western parts of Germany.
Invading the Netherlands would have been more than little pointless. The Spanish had been warring there for decades already, to rather little avail - the TYW was one of those periods when fortifications *really* counted, and tended to utterly frusrate many an ambitious campaign. Sending German troops there would merely have diverted resources from fighting the Emperor's domestic foes and bogged them down in the morass. Heck, despite having to maintain pressure on the Dutch front the Spanish Habsburgs were nonetheless perfectly capable of sending substantial troops and other resources to the aid of their German kinsmen anyway...
The Emperor could most likely have walked all over Denmark if he wanted to - indeed, I seem to recall there having been a brief skirmish between the Danes and the Imperials, which persuaded the former to remain uninvolved - but would then run into the exact same problem as the Swedes did late in the war when war broke out between them and the Danes. The hardened Swedish main field army in Germany, quick-marched to the Baltic, brushed aside all resistance with contemptuous ease... until they arrived at the shore. The thing is, the Danish "heartlands" were on the islands; and they were *the* naval superpower in the Baltic. Having a land army zillion times as strong as theirs didn't amount to zilch if you couldn't ship all those buggers over the straits in the face of the Danish navy...
In a sense the "teams" were rather set from the start of the war, and there was likely very little the Holy Roman Emperor could do to alter them. He was pretty much quaranteed the aid of his Habsburg kin in other realms, notably Spain and Austria, so much as their own issues (like the Spanish war in the Netherlands) allowed them to spare. The French Bourbons were pretty much quaranteed to happily support just about any enemy of the rival dynasty. The Swedish entry into the war, while not exactly quaranteed, was highly likely given the ambitions of its leaders and its rising stars; that that entry, should it happen, would be to the detriment of the Habsburgs, *was* a given, and the interests of the two dynasties were too diametrically opposed for there to be much possibility of "talking it out". The Danish were opportunists; mostly they were content to tax the trade passing through the straits, but weren't adverse to some military adventurism if they figured they could get away with it - both the Imperials and the Swedes had to divert armies to see off these ambitions on occasion. The Poles didn't really even care; I understand the reigning king would have been quite keen on meddling in the German war, but was bluntly overruled by the nobility who could see no point in such risky and expensive projects. The Dutch, well, they had their hands full holding off the Spanish, but other than that they made an absolute killing selling supplies to the foes of the Habsburgs... The English seem to have maintained a total hands-off approach to the Continental troubles.
And the political map of the Holy Roman Empire itself was an utter mess even at the best of times, with endless petty freetowns, baronies, sprawling fiefdoms, Papal holdings and God only knows what else with their monumental tangle of privileges, agreements, dues and so on making it hard to keep track of and steer in some common direction even when half of it wasn't in direct armed rebellion against the Emperor... Catholic lordlings tended to side with the Emperor, and Protestant ones usually sided with each other against him, but that wasn't even close to a given (many were only too happy to sit in the sidelines and try to pick the winning side) and the sheer naked political opportunism involved would have made Macchiavelli lift a quizzical eyebrow.
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