Early game:
Farm like crazy, get a single lane if you can get it, constantly spam your mace of spades and siphon of destruction, to keep your shield high. If any enemy looks like a valid target, burst them with all that you have, dealing your incredible damage. If you have pushed your minions all the way to their tower, as you often will have, use siphon of destruction on the enemy champs, and then quickly run out of tower range so it can't shoot you. harass and farm constantly. Perhaps get a jungler or another player wanting to gank to your lane, if you're having problems finishing the enemy. Gank.

Mid game:
Keep on farming for as long as you can. the more items and kills you rack up will stack leviathan, and increase your tanking efficiency. You are morde, and therefore invincible so don't die. ever. If the game is starting to lean towards teamfights, gather your team in the midlane, and walk in the front of your team, and push. push push push push push. If any enemy enters your range, hit them with siphon of destruction, mace of spades, ignite and children of the grave. Get ignite on the target first, preferably. Such an insane burst will take down most enemies quite easily. And the heavy dot and healing reduction often finishes them off even if they manage to escape. As soon as you get a slave, use it to push and tank the tower. If your teams small purple minions have run out, the tower will automatically go for your slave, thus ensuring you maximum time smashing the enemy towers. Due to mordekaisers insane pushing, you might win in this stage.

Late game:
really not the big change from the mid game. the trick here is to gather your team, and push as a well cooperated unit. If you can get baron's buff, and enslave an enemy ad carry (preferably) your team can run straight for the towers before the nexus, and even the nexus, if you have pushed that far. Your most sacred job is keeping your teammates safe in this phase. use randuinn's omen, charge in front of your carries when diving towers, and running for kills. Use creeping death as support, and put it on melee teammates farming, yourself when farming or pushing, or just before randuinn's omen, to get half a second more slowage, and on anyone taking magic damage.

If you get 20 stacks of leviathan, you can bask in the glory of insane damage reduction. 19% of all damage negated, 20% of all autoattacks avoided, attack speed reduced for people attacking you, Incredible health regeneration, (according to this website) 69% reduced physical damage and 64% reduced magic damage, and roughly 4000 hp.

Items almost always have to change from game to game. Get these items as other options, if the game dictates it:

Guardian Angel
Thornmail
Quicksilver sash
Aegis of the legion
Warmog's armor

And, choose ninja tabi especially if you use dodge runes. If you don't like dodging, (and getting the speed buff therefrom)

get health per level seals, and change your boots to mercury's or whatever you want.

Advantages of dodge:
20.75% dodge chance is great for these things:
* most ad carries cannot get their attacks through to you. You essentially take 20% decreased damage from ad carries.
* Kog'Maw's bane. a fifth of his attacks won't hit you and deliver it's deadly, deadly percentage damage. generally, this also works for madred's.
* Each time you dodge, minion or not, you get increased movement speed. You need it to charge after enemies.
* Con: Your randuinn's omen's on being struck effect isn't used as often. To counter this, build the item through heart of gold first, and then make a sprint for the full item, and primarily use the active effect.

some won't like dodge. but this list says why i love it.

Total:

19% of all damage negated, ~20% of all autoattacks avoided, attack speed reduced for people attacking you, Incredible health regeneration, (according to this website) 69% reduced physical damage and 64% reduced magic damage (not counting creeping death), and roughly 4000 hp.