Here are the two things you need to do to wipe out the Turks:

1. Kill Sultan Jalal in an open battle outside Iconium (how you do this is explained later). Can be done on turn 3.
2. Assault or use a sally-out exploit on Caesarea, killing the Crown Prince. Can be done on turn 5 or 6, depending on how you go about taking Caesarea.

First, move the entire garrison of Nicaea as far east as it will go. Hire the following mercenaries: 1 armenian archers, 1 Alan Light Cavalry and 1 Turkomans. Do as you please with your other forces, as this army will single-handedly take down the Turks. On turn 2, simply continue moving them towards Iconium:


Turn 3.
9 out of 10 times you will notice a meagre army standing right outside Iconium. Attacking it will draw out Iconium's garrison, meaning you don't have to waste a turn besieging it. Attack it and you will find yourself in a battle where you have the greatest terrain advantage ever.

The Battle of Iconium
In my case the force outside Iconium consisted of one unit of horse archers, one peasant archer and some spear militia. The Byzantine bodyguards are powerful - really powerful. Charge them straight into the archers/infantry and send the alan light cavalry to attack the horse archers. Do not worry if your light cavalry miss them, the horse archers will eventually run to the red line where you can catch them.
Run down as many troops as you can. If there is less than 15% of each army left over then it is utterly gone.
Once the first army is dealt with, you have a long time to position your troops. Sultan Jalal's reinforcing army has a long way to march to actually reach you:
Position your Byzantine Spearmen facing down the hill, with your archers on the summit near them. You want your archers to have a clear shot at the enemy once they arrive. You can put your spearmen in a schiltrom formation which will make them excellent at keeping back the Turkish infantry (and their fearsome general). Be sure to kill their archers if doing this.

The moment Sultan Jalal is in range of your archers, shoot him. At the most you will slaughter half his bodyguard. At the very least they will have fewer hitpoints left to fight. If you kill him, the other troops will crumble away like a wet cake. Run them all down and you will have taken Iconium on turn 3. Leave everything except one unit to prevent riots and move on.

Once you take Iconium (and perhaps sack it) you will have enough money to recruit a couple more mercenaries. You should recruit Alan Light Cav whenever available. Do not stop for a moment of rest!
On turn 4 your cavalry is in reach of Caesarea, but the infantry are not. This is not a problem. Simply send your general to besiege it, and then bring in the rest of the army. Otherwise you are only able to get right outside the castle, but you cannot besiege it.
Build two rams and three ladders, recruit any other mercenaries available.
You could win by auto-resolve or just fight the battle, it depends on the size of the garrison. Luckily some of the garrison had headed east.


Aaaand there you have it. Iconium taken on turn 3. Caesarea besieged on turn 4. Caesarea taken on turn 5. Every Turkish family member killed on turn 5 - and therefore the Turks are destroyed on turn 5.
Hope this has showed you the value of striking early and mercilessly!!