I wouldn't pick him personally, nor top nor jungle. If you were to play him top, I'd rush Doran's Blade into Ninja Tabi and Trinity Force, followed by Zephyr for movespeed and tenacity. You just want to build as much 1v1 power as you possibly can in order to splitpush.
All credit to trick2g for this approach.
EDIT: Don't forget to upgrade your boots with alacrity early on for extra movespeed.
yeah dorans and rush trinity for sure. like every time. zephyr is solid. botrk is good in certain circumstances, but in any case i would never play him top anymore. too many mana-less champs dominating top and even the ones that use mana use less than udyr. jungle he is still decent and i have watched trick run him since the feral flare changes and he was still beast but you really have to play him in a particular way.
From my own experience playing Irelia I have always preferred zephyr. These two champions are surprisingly similar in their 1v1 splitpush style. Zephyr allows you to go for different boots and ninja tabi are super good in a 1v1 scenario.
You would pick Udyr in general if the enemy team has little to no CC OR if your team has a high amount of CC. The reason I say this is because Udyr is not as mobile as other champions. Sure, he can run very fast, but other champions have dashes.
In the current meta, Udyr is susceptible to kiting due to the large amount of slows, stuns, and snares. The only way you can make plays as Udyr is if you Flash or if your teammates can lock them down for you.
Pick Udyr at your own risk if you want to play to win. If you want to play Udyr for the sake of playing, then oh dear . . . disregard this comment entirely.
All credit to trick2g for this approach.
EDIT: Don't forget to upgrade your boots with alacrity early on for extra movespeed.
In the current meta,
Pick
Have fun on the rift!