Austria
Austria is an interesting Nation in EiA. It's not quite one of the big boys, but a cut above the smaller nations. Corps structure is a little soft, but the good Austrian leaders make up for that. The dual Grenadiers are a major boon to the Austrian player, allowing him to put two decent armies into the field. Enough preamble, though, on to my diplomatic notes.
Great Britain
Austria, due to a decided lack of coastline, is probably least likely to go to war with Britain. However, relations are not always warm, and, if you adopt a "soft" policy with the French, the British may cut off your supply of finance. Of course, due to your robust economy, British funds are more of a luxury than anything else. Be nice to the Brits, but make sure they're actually giving you something for your support.
France
I don't recommend a hard-line attitude with France. Sure, you'll end up fighting him a lot, but a "war to the death" attitude isn't profitable - it's a lot more likely to be your death than his. Instead, talk to France a lot, make noises about only fighting him for your allies (even if you're the one organising the coalitions), and don't be excessively cruel if you end up getting a surrender from him - leave the army untouched, and only exile Napoleon if the British insist on it. Ideally, get them to give you some money for it, as well. Why be so nice to the French? Because, in theory, they'll return the favour. Being able to get away with a Conditional Surrender when fortune looks the other way is nothing to be sneezed at.
It's also quite possible to work with the French - your help is invaluable to them in attacking Russia, and gives them the option of attacking the Turks. For your part, fighting alongside the French should net you enough Victory Points for at least a combined victory. And, if you're canny about it, your "traditional" allies might be in good enough shape to help you knock France down again. Then again, they're more likely to be baying for your blood, so I doubt that you'd get the chance to turn-coat a second time.
Prussia
The Prussians normally follow the Austrians' lead in EiA, fitting somewhere between an annoying kid brother and a valued ally. If they're the former, then don't hurt their feelings, unless the Russians have already. A Prusso-Russian axis makes Austria feel decidedly less secure. If the Prussian player is more mature, then you can afford to do your own thing a bit more, and just touch base with him every so often. While there are some gains to be made out of fighting Prussia, they're not worth enough - unless you're turning to the dark side, in which case you'll probably end up with the Prussians coming after you with some vengeance. Not to worry, the French will help you out - if only out of their own self-interest.
Russia
Relations with the Russians tend to blow hot and cold - on the one hand, you have common interests, fighting the French and the Turks, on the other, the question of Russian Dominance all too often rears its ugly head. Don't cave into them early - if they threaten war, tell them that you'll go to the French for help if they do. The counter-threat will probably cool them off, even if you don't have the option. Later on, assuming the French are taking time to lick their wounds, it's probably better to support the Russians in a Balkans campaign - better the Turks than you, right? If they're not, then you can keep your options more open, claiming that you need to rebuild after your defeat. Depending on the personality of the Turkish player, it may be necessary to force a conditional surrender on him, simply to ensure your borders for confrontation with the French menace.
Turkey
To be honest, I lean towards ruthlessness with the Ottomans. Sure, smile and wave a white flag in the beginning, while he's a threat, deal with the French (one way or another), then roll east and knock the Turks down a notch or two. Their VP target is far too low, and besides, you need the extended peace & other goodies from his surrenders. I suggest being fairly lenient, only asking for Conditionals, because trying to force Unconditional peace on Turkey is a right pain in the ass, and the troops you lose doing so would probably be better deployed against France, or even Russia. Besides, if you're only being marginally predatory, the Turks won't resent you (much).
Spain
Well, what's he good for? Ok, you'll probably never have to fight him, but there's not a lot he can offer you. Maybe support in Italy, against the French - especially if the bulk of your forces are fighting alongside the Prussians. And I suppose he can screw with the Turks, but that's naval stuff, and Austria can quite happily not build a ship all game. Still, there's no point in getting aggressive with Spain, you might as well be Allies, even if you don't do a lot for one another.