It really depends on how you decide to play and build him. Personally, I tend to use the following setup for Phoenix jungle.
Runes: MS Quints, Atk Speed Marks, Armor Seals, Scaling MR or Scaling CDR Glyphs
Masteries: 21/0/9, 9/21/0, 21/9/0, 0/21/9, or 0/9/21 depending on what I want to do and who I'm against
Skill Order: RWRERR, R > W = E > Q
Your item build is very versatile. Personally, I would probably recommend building Devourer into Sunfire Cape and Mercury Treads for damage, clear speed, and durability if you are even or behind. At this point, you can build Trinity Force pretty safely since you are already fairly durable between Sunfire Cape and Turtle Stance.
Devourer into Trinity Force and Mercury Treads is very powerful, but I think you want to be ahead before getting damage that early. However, after those two items I'd recommend getting defenses and CDR; Frozen Heart and Spirit Visage/Banner of Command are great items for this.
Personally, I tend to use Udyr as a split pusher. Once you have Frozen Heart and Trinity Force (and maybe another armor item) you should be able to solo towers without minions pretty easily by alternating Turtle Stance and Tiger Stance. If people try to stop your splitpush, Udyr is a strong duelist so he should be able to kill them or just use Turtle Stance and Bear Stance to escape.
For damage, attack speed is probably your best bet. Trinity Force, Zephyr, Blade of the Ruined King, Wit's End, and Devourer are excellent items on Udyr.
If you want to see Udyr in action, Trick2G is probably your best bet. He's pretty renown for maining Udyr and uses a variety of builds and playstyles on him.