Hello. I am Mace 0f Spades, a brazilian diamond Mordekaiser main. HUEHUE
That's pure coincidence, I swear. There are only a few people that play Mordekaiser in Brazil.
Mordekaiser's potential to solo-win games is very high. Yes, it is.
If you play him right you should dominate melee lanes and survive ranged lanes by pushing and poking, and at late game punish your enemies for ignoring you in team fights (very common if you don't play like a dumbass)
I will try to make this guide not focused on very in-depth details, and yes how you should play Mordekaiser so you can always have a good laning phase which will lead you to have tons of damage.

You max W first for the very good sustained damage (its good either for pushing either for trading against melee champions) and sustain in the second cast. You max Q second because it scales better with levels than E does. Obviously you max E last.
Always upgrade your ultimate when you can.

You should bring Exhaust when you are against a melee champion, and ghost when against a ranged one.
Don't take teleport even if you are in the top-lane, as the Teleport now takes 4.5 seconds to cast and this is too long for an immobile champion like Mordekaiser.

Melee lanes are very easy for Mordekaiser if you play it right (except Jayce and Kayle obviously)
At level 1, learn W. Wait for a friendly minion to get low, and when you see your enemy laner coming to get him, use your W in a friendly minion that is NOT low and that is close to you, then, let your W deal damage to your enemy (make sure you are close enough to the minion that you casted W so you deal the damage) until he is getting away, when you see he will get out of your W, you should cast it again so you heal more (it heals more when there is an enemy champion inside of it)
At level 2, if you got exhaust, you can get a kill. Upgrade Q and do the same thing, wait for your enemy to come farm a minion, then W in a friendly minion that is not low and is close to you, your enemy will probably try to trade with you near the minion that you just W'ed, so activate your Q and when he see that he is losing, he will try to run away, so you just chase him with your Q trying to burn his flash (sometimes the 3rd Q can get a kill for you)
You should do this the entire laning phase against melee. Basically, as I just said twice, you wait your opponent to go for a CS, and do insane damage with your W, and chase him with your Q, and E when you can. With ultimate will be pretty much the same thing.

You can't be kill hungry in this kind of lane. You should just push your lane and poke your opponent with E when he goes CSing so you can gain lane control.
At level 1 you will learn W and cast it on a friendly minion that is taking less damage from the enemy wave, and will stand in the middle of the wave. While you do this, you will be generating shield so you can ignore auto-attacks, you should just care about dodging skill shots (take care with champions like Cassiopeia which can deal tons of damage at level 1)
You do this because if you don't push the wave at level 1 you will be zoned by ranged champions, so you take CS before they don't let you.
At levels 2 and 3, upgrade E ON BOTH of these levels, so you can poke your opponent when he goes for a CS, gaining lane control. Keep using W for pushing lane and generating shield, but do it only when your E is on cooldown.
At level 4 you get your Q, after this just max W.
Sometimes your enemy will overextend for poking, so you can cast your W on a minion and turn on them and do unexpected damage (for them), forcing them a flash or getting a kill.
You will still deal more damage than your opponent even if you don't kill them in laning phase (that doesn't mean having a bad laning phase), the only thing you have to do is play right in team fights.

In teamfights as Mordekaiser, you have to be patient. Don't try to flash alone in someone and burst it, as it will be a waste of potential. Instead, wait for a bruiser or a tank of your team to engage. When he does, cast your W on him and dive the enemy team with him. WHEN THERE ARE MANY CHAMPIONS INSIDE W, re-cast it as it will provide you or/and your ally tons of healing, which can lead to winning the teamfight. You should have your priorities when you ultimate, always ultimate the guy which have more damage in auto-attacks (usually the ADC, but can be something like Yasuo or Yi). Use your 3 Qs on someone that you actually can catch.

When you got your dragon, DON'T use him to stupid things like farming jungle camps. You can use him to:
- Push turrets
- Solo baron (dragon tanks, you will have enough damage at 20 minutes)
- Dive if your team is ahead
- If it's happening a team fight in dragon's pit, CTRL + Right Click someone that has to be stopped. Your dragon will focus who you clicked in until this guy is dead or gets in Fog of War.

This guide is Work in Progress.