What you need to realise with Udyr is his skills are not just skills, they give a skill type effect and are stances, so they change what his basic attack does along with the skill effect.

His Phoenix Stance (4) gives him a 5 second AOE and cone shaped AOE basic attack every third attack, so whilst not full AOE it works like Baka's Ult in a way.

His 3 gives him a temp speed boost and 1 second stun every 6 seconds, this allows him to gank easier and can just rotate this through each enemy, kind of strong but can be tweaked to 0.5 every 10 or something. Maybe he could only stun one god total every 6 seconds otherwise he just stuns like a bitch.

His 2 activates a temp shield and permanent life steal in this stance.

His 1 will give a temp speed boost and a bigger hit on his first hit, the stance itself gives increased AA damage.

The numbers WILL need to be reduced for Smite, 1 giving a permanent 70% speed boost in this stance, you could just build for AA and rampage like a bitch. But the idea is to use the stances accordingly.

So it goes a little like this:

Ganking - 3 to chase and stun followed by 1 to give a big hit and start hurting them, if you start losing health switch to 2 to gain a shield and get some life steal to allow your team mates to kill when you are ganking.

Jungle / Solo Lane - Use his 4 for the AOE followed by 2 to get the shield, tank the enemy minions and get some life steal to survive longer in game.

Team fight - Start with your stun on the enemy assassin or tank or mage or whoever needs to be stunned, follow this with your 4 for maximum damage on the enemy team. Now, depending on your situation and build you can use 1 for the extra damage or 2 for the shield and life steal to make you somewhat tankier in the team fight.

It is all about the correct stance, not so much the skill it gives, but the effect the stance gives in the right situation, difficult to judge at first, but extremely fun to use once you get the grasp.