My way of Offtank Mundo.
This build focuses on survive ablility because a dead mundo is useless.
I don't recommend damage items on Mundo, because Mundo has no scaling with damage (except the pathetic AP ratio of Burning Agony) and with Masochism and Infected Cleaver he has all the damage he needs. The only damage item i would recommend is Sunfire Cape or Atmas Impaler as 6th Item.
As Mundo we want to become UNDEAD. You want your enemies to fear the never dying Mundo!

Should be self explanatory. Armor Pen for his high AD witch Masochism, Health per Lvl because we are Mundo and CDR per Lvl because we need as many CDR as possible without sacrificing other stats - but only after reaching lvl 11. Before lvl 11 CDR on Mundo is pretty useless, because his Ultimate at rank 1 isn't good for tanking damage but for staying alive.

Offensive and Utility masteries aren't as usefull as Defensiv for Dr. Mundo

Everything Mundo needs during Early game is HP. Not Health regen or resistances, no, just HP.
And please don't build Spirit visage as your first item, because its boosts are useless before lvl 11.

Randuins Omen has only usefull bonuses for Mundo, aswell as Force of Nature.
You can build Atmas Impaler or Sunfire as 6th Item if you like.
And please don't build any other MR Items than 1 Force of Nature! With FoN, Spirit Visage and Mercury Boots we have all the MR we need.
Thornmail is one of the most situational Items in the game. Build it as 6th Item if their glass cannon AD is raping you! Otherwise Randuins, Sunfire or Atmas are much better.
A 2nd Warmogs or a Guardian Angel are also good 6th Items.

If they dont have real CC you can trade your Mercury Boots for Boots of Swiftness.

Sadism > Infected Cleaver > Masochism > Burning Agony

Don't invest skill points into Burning Agony too early. The CC reduction is too low at low ranks, the damage is not compareable with Infected Cleaver or Masochism and you will kill yourself if you don't have the HP regen.

Ghost because Ghost + Sadism + Infected Cleaver = Super chasing / Super running away
Replaceable with Flash because Flash is op. But i don't recommend it.

Exhaust because Exhaust + Masochism + Sadism + Infected Cleaver = Get a kill
It's also usefull for countering that ******ed Carry or Caster that deals a billion damage and it makes you a real deal during Early Game (and also during Mid and Late, but then you will be a strong even without it...)
Replaceable with Ignite if you think that Ignite will be more usefull.

Early Game you should check bushes with Q, place wards if they have a jungler and remember to have an eye on the minimap.
During Laning phase you stay your Infected Cleavers range away from their minions. If they close up to harass let them taste your cleaver and go back a bit. That means that you won't get harassed and harass them.
Try to lasthit as much as you can with your auto atacks. try to do not use masochism for farming and don't risk your live for a minion kill.
If you get outzoned or they dominate the lane farm with your Cleaver and harass them with your Cleaver as i already told you.
If you dominate the lane, use your Cleaver to outzone them. Try to do not push too much and care for ganks.
If you can kill someone without dying you better get the kill.

Mid and Late game you can farm with Masochism, Burning Agony and Infected Cleaver.

Really Simply. Most of the time you cannot initiate a teamfight. If a teamfight breaks out, it's your job to slow them with Randuins and jumb on their most dangerous damage Dealer.

For Example:
Teamfight. Their fed (and squishy) TF uses his Ultimate to join. So what do you do? Throw your Cleaver into his Face and start raping him. If he stays he will die, if he runs away they will lose their most important damage dealer. Hunt him and try to kill him. Remember: Your team will lose its offtank for a while but they will lose their carry.

In generell you should jumb on their carry and make him cry. If you like exhaust their Caster if he performs his Combo. You have Randuins to slow them and making their AD Carry cry.
It is not your Job to protect your team. You are the Offtank not the Tank or the supporter.
Just go for their Carry.
If they have more than 1 dangerous Carry (for example Akali and Yi) you go for the carry that is more vulnurable against you. Exhaust the other one and make your Team focus him.

-Your Infected Cleaver actually has a higher range than the range that is shown. This knowledge and some training will make it much easier to farm with Q and harass them.
-With Masochism you get more dangerous while being low Hp. Especially in Early game your HP will drop fast, but that makes you hurt even more. So you're much more dangerous than most other champions during the laning phase.
-If you pop your Ultimate and die and you are revived by Guardian Angel or Zileans Chronoshift you will still regen Hp during the revive animation. Don't know if that's a bug or if they already fixed it.
-Your Infected Cleaver deals great damage against high HP oppenets. That's really usefull if you want to kill the Red buff Lizard, the dragon or Baron Nashor.
-ALWAYS check bushes with Q and NOT with your face!