Udyr is an interesting champion, he has no real Ulti since you can choose his phoenix stance as starting move as well and you can choose for yourself which skill only reaches lvl3.

I start out with the Bear Stance but if you want to Jungle (and in this case I would replace Stark's Fervor with Wriggles Lantern building up madred's razor as your first item and replace either heal or Fortify with Smite or Ignite) I'd start with Phoenix stance for it's sunfire cape like activate and it's passive that deals damage to several monsters at a time.
Oh btw, I made this mistake myself, for people who don't know Udyr, his skills say "Persistent effect" but it's not a passive, it's only active as long as you're still in that specific stance.

Like I said I normally start out with Bear stance and Vampiric Scepter. The lifesteal helps me to stay alive and in action for a little longer and gives me the ability to keep low and get back some health without recalling why the bear is a good starter because of the stun.

I build Udyr as a Lifesteal Tank becuase of the high attack speed increase when you activate Tiger which meant that I wouldn't have to build alot of attack speed and because you can just switch over to Turtle Stance when you need to regain your life a little faster.

Udyr is a great champion for ganking and chasing thanks to his Bear Stance because of the movement speed increase and the stun. He is also a great minion killer thanks to the Phoenix Stance with it's AOE damage. On top of that he can increase his damage output with the attack speed and special hit of his tiger stance and can get his life and mana back up with the Turtle Stance which also gives him a shield to block incoming damage.

This all makes Udyr the perfect champion to build on Tanking and Damage though I prefered Life steal Tanking which works great for me, but let me explaine my build more thoroughly:
Udyr is a Champion with all-round possibility's.
-Thanks to a good combination of Phoenix and Tiger combined with my sunfire cape, minions go down fast without me running out of mana by adding well placed Turtle Stances
-With the increased attack speed of Tiger Stance Turrets go down fast especially with the damage and attack speed from my lifesteal items and you even don't really have to worry about opposing minions killing yours or damaging you a little to much cause you can just activate Phoenix Stance once in a while which should (together with Sunfire Cape) kill them quite fast even with you still hitting the Turret.
-Thanks to my high Lifesteal and the lifesteal and Shield from Turtle Stance, I can fight enemy's without loosing lots of health.
-With Sunfire Cape, Lifesteal Items and Phoenix Stance, Jungling is a piece of Cake
-Bear stance alone makes a good chaser, but with 2 bloodthirsters I can actually kill them as well.

now, my summoner spells. Udyr doesn't have much need for the obvious choises like Clarity/Teleport/Flash/Ghost so I was able to choose Fortify, which even helps me kill opponents by stunning them and icreasing my turrets damage output.
The other is heal. I use heal mostly when I'm a tad late with switching to Turtle Stance. If you're getting low, Heal and Turtle can still get you back.

Well, Hope you enjoyed and feel free to ask for more information
-StrayBee Out-