This build will make you almost unbeatable in Twisted Treeline, sometimes even if your two teammates sucks a lot, you easy carry the game to the victory. The capacity to jungle and 1x1 any champion will make playing Udyr a lot fun. It's very simple to play too, since the only two skills you will use will be Tiger and Bear Stance for everything, Turtle Stance when you know that you will be hard damaged or when you run out of HP/MP and are alone in the lane for recovering. Phoenix Stance will be used for farming and jungling, and even when your weak enemies surround you, using the area damage on your favor.

Pros
• Extremely unbeatable in 1x1
• Good survive rates
• Strong in team fights or when alone
• Great Life Steal!
• Fun and easy to play

Cons
• Will be focused almost everytime
• Mana problems in Early Game
• You will take hard damage in Early and Mid game
• Item Dependence

These are the best Summoner Skills in the game in my opinion, but if you like Flash more than you like Ghost, will be nice too, but Exhaust is the main Summoner Skill and can't be changed.
Sometimes, champions will escape of the burst damage of Tiger Stance with ridiculously low health, so you can choose Ignite as well, but have in mind that Ghost/Flash will be missed.

The Bear Stance start will help a lot in ganks in the start. If you had Exhaust, just few champions can escape from you in any part of the game.
The only thing that can be changed in the skill sequence and still doing great is lefting 4 points in Turtle Stance and putting one more point in Phoenix Stance, if you want to... That's not what I used to do, since the Life Steal of Turtle Stance is huge, and will be of very more utility, but you free to choose.
Getting Bear Stance will help a lot in first gank fights, since you can stun enemies. You'll see a lot of Tiger Stance here, since it's a DPS Build. Don't bother about the no use of Phoenix for anything but Farming and Jungling...
Tiger Stance will do unnecessary damage with this build, even in the start. In mid-game it's impossible to 1x1 you, even Warwick will fall at your feet and as soon as you get Tiger Stance Lv 2 you can solo the Dragon at Twisted Treeline.

Those itens will do great on Udyr, and Wriggle's Lantern is a surprise right? When I first done Wriggle's I was surprised on how much effective it was for Udyr, mainly in the Early Game. The armor, the damage and at last but not least the Life Steal. These stats are perfect for Udyr. Now come the cons: it's a starting item, so raplacing Wriggle's Lantern with a Hextech Gunblade will finish the enemy team. At this point, 1x1 with you will be avoided even for Tryndamere or Warwick. Keep this in mind, but just replace it when you end all of the other itens in the build.
Berserker's Greaves still give headaches, I never know if it's better going for a Mercury Treads or keeping Berserker's. But currently, I'm going for Berserker's and everything is alright, but feel free for doing whatever you want on boots.
Madred Bloodrazor give you survivability for all the rest of the game. Will increase your harassment level, boosting Attack Speed and Attack Damage. Following the sequence of Madred Razor > Recurve Bow > Pick Axe is important, since Attack Speed is more important for Udyr.
With The Bloodthirster, you will be doing horryfying damage as well you will be almost unkillable with your Life Steal.
The Black Cleaver will give you Armor Penetration and Attack Speed... nothing more to say. At this moment, if the game is keeps on, Surrender Votes will be occurring insanely in the enemy team, and enemies will be cursing you with names that I don't want to say here.
Phantom Dancer is ultimate! Attack and Movement Speed will do a lot of Rage Quits from enemy's side.

Thanks for giving me your attention! Good Luck and Have Fun in Fields of Justice.