Xibei San Ma
Austria is small, poor and underdeveloped. Furthermore it is seen as little more than a pawn by Italy and Germany, two of your neighbours. You need to plan each step wisely if you want to survive.
Walkthrough for 1936 Scenario
I have played several games with Austria, and each one has played out very similarly.
Modding Activity to Consider
You may (as I have done) consider modding the HoI2 files a little to give Austria more options later in the game. One thing you can do is to make Austria the "true owner" of Hungary, which means you will inherit all Hungarian units when you annex Hungary. It is also not a bad idea to make all provinces of the defunct Austro-Hungarian Empire "national" provinces. You should add at least two tech teams - a naval academy and a naval arsenal. I made them to appear in 1937, as by this time you will have access to water again.
You could also consider giving Austria some basic naval technologies and doctrines. They had a navy until 1918, so this is not ahistorical by any means.
War From the Beginning
As soon as the game starts, become more interventionist. Research better infantry, and whatever else you see fit.
Move all your troops to the east, and declare war on Hungary. You should be able to reach the Danube and occpy everything up to it easily.
At some point in this campaign, Italy will most likely declare war on you. Germany then usually declares war on Italy, since they guarantee your independance. This is your chance for Austrian world dominance - enter the Axis and try to assume full military control of Germany. This has always worked for me.
Turning the Tide in the Alps
Now, you govern tiny little Austria, but command the entire German Wehrmacht. This means that for your frustrated field commanders in Hungary and your panicking civilians in western Austria (who are probably being overrun by the Italians) a dream has come true - a real army can save Austria.
Move the entire German army into Austria except for 8-10 divisions to guard the French border (this will be important later!). Split off maybe 6 German divisions and send them to Hungary to help cross the Danube and annex Hungary. The rest should enter the Alps, and begin the offensive into Italy.
Since the conquest of Italy begins from Austria, all of Italy will fall under Austrian control. The conquest of mainland Italy should not prove too difficult, as the Germans are enormously strong, and can be supported by the Austrian army and the German expeditionary force from Hungary if you run into difficulties.
Once Italy is under your control, you need to build some sort of navy, especially transport ships. This is where modding the game comes in useful, as Austria otherwise has grave difficulties doing this. Well, you can get transports anyway.
The snag so far is that Italy is merely Austrian-controlled, it is not part of your territory and you can't deploy any ships there. So you need a port, and quickly. Array your combined Austro-German army around Yugoslavia and attack. Leave enough troops as a garrison on the Franco-Italian border in case the Allies declare war on you. This can happen.
Annexing Yugoslavia should not take long, or be difficult. Greece and Turkey (or other Balkan states) may declare war on you, if they do, onwards with your conquest of the Balkans.
Sooner or later, your first transports and destroyers will be ready, and for the first time in twenty years an Austrian ship will sail to sea! Use the navy to invade Crete, Libya, and if necessary also Ethiopia, to annex Greece and Italy.
By now it should be early 1937 or so, and Austria rules the Balkans and has access to numerous naval bases in the Mediterranean.
The Great War
You should keep checking whether the Germans are building new units (they are, obviously!). They will invariably deploy them in Berlin. Send them to the French border (north and south of the Alps). It is only a matter of time now, before the Allies declare war.
When they do, it should be common sense to attack south of the Alps, so France becomes Austrian territory as well. This fight will be incredibly hard. You may suffer some setbacks in the beginning, but persevere and all will be well.
After that, you can try attacking Czechoslovakia, Bulgaria and Romania, although once again some modding will be useful unless you want to see the entire "Sudetenland" in German hands after a bloody war in which primarily Austrian blood was spillt.
Now everything is up to you. You have a powerful European base from which to launch further campaigns of your own, or with which to support the Germans (especially against the Soviet Union, even more so if you happen to be in control of Turkey).
An option to consider is releasing Ethiopia, Somalia and Libya as independant states, as they can raise hell in Africa and provide at least some research or units. The colonies as they are are merely sand, when they are released they get 5 IC from "Heaven".