Couple of things on top of what demon mentioned.
1. Your first slider move as Ottoman should always go toward narrowminded. Because with a theologian, you can now activate two religious decisions.
One reduces stab cost by 5%, and increases yearly missionary by 0.5 but increase missionary cost by 6%.
The other reduces missionary cost by 4%, and increases yearly missionary by another 0.5, at the cost of +1 revolt risk.
These two will counter your future innovative moves, and bring you enough missionaries to convert your orthodox provinces.
2. NEVER let your infamy go above 10 unless you absolutely have to, especially when you're ready to westernize.
3. Venice needs to die as early as possible. I tend to try and annex him in two wars after building enough cogs, and release him as a vassal. He's the greatest fodder against HRE people, as you'll see several doom stacks trying to get to Venice that's being stopped by your 1 cog, and you won't suffer any WE due to occupation.
4. Cavalry Calvary Cavalry. Your cavalry out ranks western ones till mid 1500s, if you haven't westernized yet by then. When you have more regiments than the enemy army, a maximum of 4 cavalry will do free damage against him, called flanking. (assuming there aren't more than 30 regiments already) Which brings up the other problem for you.
The maximum width of a battle field is 30. When the enemy army has 25, it won't matter if you outnumber them 3:1. Only 25+maximum of 4 calvaries will be able to do damage to them at a time. And trust me, the AI battle system is really bad at rotating regiments in and out.
What does matter is that you can have 3 army stacks of 25 infantry and 1 with 4 cavalries, and rotate your infamy army stacks. It'll allow 2 of your infantry army to regenerate number and morale while your 1 infantry/cav army are doing damage/taking a beating.
I generally do army stacks of multiples of 2 inf 1 cav, because it's much easier to manage with the split stack function.
3. As Ottoman, you're almost always going to lag behind in tech. It's generally a good idea to focus on just government and land tech until you're westernized. Which does make defender of faith a good idea as the negatives won't affect you as much.
4. Legitimacy advisor is bad, unless you're mass PUing the Muslim nations (like you should to strive for from the start of the game).
PU is the most powerful tool for Ottoman, because nearly every Muslim nation west of Timurid is of Ottoman's culture group. Meaning. That means when you do inherit those nations, you automatically receive free cores and preserve all buildings. Assuming Castile hasn't done enough damage, you should get a bunch of provinces with full t1 buildings.
With those nations under PU, it also prevents Castile from blobbing the entire northern Africa, cause you'll automatically become war leader, which prevents some stupid territory loss.
5. You need a diplomat and an embassy. They increases your limited infamy reduction, which you need desperately if you wish to expand through war.
6. What did you do to your infamy! With my count you only had to spend 14 infamy + w/e Georgia had (assuming you annex instead of colonize GH land). Don't ever spend more than 2 infamy per province, especially when you need just 1 against those provinces with Holy War CB.
7. Military Drill. You need this NI to survive. Against Timurid, GH, and eventually Bohemia/Austria. Once you've gotten enough stability, swap out National Conscript with MD.
8. Inflation. Going above 5 is frowned upon by everyone, and never go above 10 unless you're Horde or absolutely need to to expand as an OPM/2PM. Don't mint more than you can recover. If you have to, build galley stead of carraks to have your naval superiority.
These are some of the long term and internal things that you've missed out on, so onto how you can beat Austria.
1. Get Venice off your back.
2. Get a new general, you're sitting at 90ish army tradition!
3. The AI is really really bad at stack management. After the first siege or two, it'll generally split them all up into stacks of 12~25 to carpet your provinces. That's your time to gobble them up one by one.
At the current tech level, your Azab Infantry is only slightly worse than Austria's unit of choice, while your cavalry is vastly superior to his. Follow the flanking mechanic, and you should be able to eat any of his stacks below 20.
4. Have 2 armies rotating in/out if necessary.
5. If 4 still didn't work, consider using bait and reinforce. Use a small stack on a favorable terrain to lure the AI over, then throw your bigger stack in, and retreat your small stack. If the AI moves to engage you, they may get river crossing and terrain penalty, which greatly increases your odd. Oltenia and Serbia are both idea locations.
6. If needed, with your navy loose due to no Venice threat, use your cogs and send them to Austria's back and distract his forces.
The game is salvagable at the 1508 save, but at this point, I would advise you to pick up what you've learned with this playthrough and start over due to the ridiculous amount of infamy + western influence.
