Obviously to take the city you'd probably have to gas it first. Are Christians segregated in Miklagard? If so, that would be very convenient. Also, unlike conventional shelling or nuclear weapons gas would not damage the structures. It would take a bit of cleanup as an effective nerve agent leaves a mess, but otherwise, everything would be in tact. Biological weapons are just too darn uncontrollable, and shelling not only ruins structures that would be better for future usage but would also create ruins - probably one of the best defensive structures ever created, albeit unintentionally. As for the rest of Turkey, nuclear weapons would neutralize their army rather effectively. If you want to go conventional, you would need probably 10,000 men armed and equiped to SADF/IDF standards. Allies are also useful. Syria has reason to be ticked at the Turks after they clean up their mess. Likewise, the Kurds and Armenians could potentially profit. Greece is kind of useless at the moment, though if a group like Golden Dawn were to take over they could have motive. Bulgaria would be better. Their army is pretty top notch, or at least their equipment is.
Now, into the real world...
In all reality, Russia is the only army that could realistically take on Turkey. If they do, it will be an economics fight rather than a military one. And this I think is a very realistic consideration. Russia has the European gas market pretty well cornered. Gazprom is probably one of the more influential corporations in the world. If Turkey were to threaten this hegemony Russia would do something.
One thing that no one has mentioned yet is that Turkey is a member of NATO. (If it has been mentioned, my apologies.) It's not so much the Turkish army that needs to be feared but the Turks + Germany/France/US/Britain/Holland/Belgium/Greece/Italy/and so on. If Turkey were to go full-retard (aka Islamist) and drop out of NATO or be pushed out, their life expectancy as a unified state would drop somewhat.
A real potential threat would be the creation of a Kurdistan in Turkey, Iraq, and Syria. The Kurds have been gaining a lot of military experience in Syria and Iraq over the last 10 years. If anything is going to hurt a modern nation state it will be a full blown insurgency. They have some mountainous regions to use as a base and could just hop the border to Syria or Iraq any time they needed to get some space. Turkish cross border attacks could spark a conflict with Syria or Iraq...and then Iran could get involved.
Taking back Miklagard is an exercise in fantasy but there are plenty of offshoots that are more plausible.