is a great jungler with good cc and ganking potential, he is unkillable if played right due to his amazing movement speed that is granted from his bear stance and passive.

PROS:
-Fast jungle clear time
-Can counter jungle fluently
-Has strong ganks if played right
-AOE from pheonix form grants good damage just for standing beside an opponent
-Hard to catch
-Excellent move speed
-Good life steal

CONS:
-Bear stances stun resets every 6 seconds on original target making it not as useful if they are below turret or have excellent mobility
-Dies against teams with hard cc and life shred

I prefer SCALING magic resist runes over just normal ones because it grants extra magic resist over time and Udyr is very good late game anyway so he needs things that help him more late game than early.

I take attack speed runes because it helps for a faster clear time and it also grants a good ability to duel as well as charge in with bear stance and get the fast attack off.

I suggest movement speed runes if you want to be very swift and be able to either catch up to your enemies OR be able to escape from them, I have been in many situations with these and been able to get out no matter what, even with tons of cc you can break clear of the enemies, of course the shurelya's helps a lot in those situations too.

I take straight up seals of armor because I like to have a little bit more tankiness early game and by the time it is late game I have already build armor so I dont need them to scale for late.

I built 9/21/0 into my skill tree because I prefer to be more tanky for my team than be a damage dealer, Udyr has a great capability to tank and lifesteal if you let him so I decided this was the way to go, also having those points into anti auto attack damage helps a lot when you are teamfighting even though you may not notice it.
That's why I have them in there and I am sure they saved me a few times aha.

Ok. I will list off every item I have you get and why I believe they are perfect for Udyr and his tanking capability.

Spirit of the Ancient Golem:
-Grants CD reduction
-Bonus damage to creeps
-Extra health
-Tenacity boost
-HEALTH and MANA regen increase

Mercury's Treads:
-Better movement speed
-More tenacity boost
-Magic resist

Shurelya's Reverie:
-CD reduction
-Health increase
-HEALTH and MANA regen increase

Warmogs armor:
-Tons of health
-Bonus health regen

Runic Bulwark:
-Helps teamates with an aura that grants boosted stats
-Armor increase
-Health increase
-Magic resist increased

Ruby Crystal:
-Bonus health increase

All of these things are very important to Udyr and I will explain why.
-Udyr needs Health to tank enemies damage
-Udyr relies on abilities so he needs extra CD and it makes them come up faster
-Udyr can be extremely tanky and last long in teamfights because of extra mana and health regen.
-Udyr's turtle form + armor makes AD champions do way less damage and you soak so much more
-Udyr needs extra magic resist for late game because AP heavy champions can hurt quite a lot with burst
-Udyr can clear faster and gank more frequently with extra damage to monsters.

I prefer not to put a point into either turtle or tiger until later in the game because of the early game ganking steroid Pheonix and Bear form put in place. You don't have to do it exactly how I do, don't be afraid to throw a point into turtle or tiger if you really feel like you need the extra sustain or attack speed but I just prefer to hold out on them.

Smite is mandatory for jungle.
Ghost is my more favored spell over flash because more often then not you will find yourself running towards enemies or coming to gank enemies who have flash and even though it may initially put some distance between you and them you can just catch up in a matter of seconds because of the boost to movement speed, you also become uncatchable by enemies with ghost because of the extra movement speed put on top of 3 stacks of your passive and your bear stance gets you a lot further away then a normal flash.
Your choice though.

As Udyr I decide to dance around with the enemies for a bit until one of them presents themselves even a BIT out of position and then I ghost and run straight into them, this causes the enemies to react and they will mostly jump on you while your team starts getting some good damage in.
By doing this you buy time and asorb damage from the enemy team that could have went to your teamate.
Keep in mind that you should go for ANY target that steps out of place, be it support or apc, just go.
After they think you are only aiming that one you can just jump on the target that dishes out the most damage on their team which is your main goal in teamfights, disrupt and damage.