The idea of using Blue colored items on udyr was a fun concept I have so much fun now I'm no pro at lol but I can still hvae fun right? Well to start off bludyr provides quite the CC and the tankyness and the damage you will need.
Runes? well i use my personal runes which i think they are ****. XD I suggest getting mobility quints armor pen marks armor seals and scaling magic resist glyphs atleast that is what i think is the best you can go ahead and experiment with the runes.
I suggest 9/21/0 taking attack speed and damage in the offensive. then take armor MR health regen and tenacity in defense.
Remember its bludyr so build one item that its not blue and you just ****ed this **** up XD to start off you need to rush the newest item that blueish :P ER aka Essence Reaver that will give Udyr his mana back which is what you will need since udyr always spams his abilities. then we need moore resistances so for boots it will be mercury treads Another MR item that you will need is banshee veil then last but not least Frozen heart will give you your armor now it matters which you will win depending on your laner or the jungler that is camping you. The next item will depend on you. You have the Frozen Mallet or the iceborn Gauntlet both provided the slow which is what you need now i prefer the Gauntlet because it gives the sheen effect. Last item you should build should be Last whisper to ignore that pesky armor. now feel free to switch it up to your style and tell me how it works out for you :) Also if you are jungling look at spirt of the elder lizard for more damage and true damage or the ancient golem for more HP and CDR but its getting reworked soon so the tenacity is being removed next patch.
As Udyr there are many skill sequences so ill give you the general idea on what to do Your Q will be in my opinion your main source of damage so I'd recommend maxing it first. your W is a shield and life steal so put points if you are getting damaged a lot and need to heal up. your E is a stun and mobility boost the stun is the same at all ranks but the movement speed is incresed so put ponits if you are getting chased while you are low. And last but not least your R is another source of damage and its the main one to other people and i agree in some circumstances put points if you need wave clear or need more damage.
Now for Spells you want to take Teleport and ghost reason so you can split push and get into the teamfights no matter the location ghost to get away from being chased now you can take flash if there is someone like J4 or that can apply lots of CC and won't let you go even with ghost. Smite and ignite(get it smite and ignite pentakil's album XD) are situational Smite for jungling and ignite for champs that can heal rapidly.
Well in summary Bludyr can apply lots of CC and is pretty tanky and can deal damage especially with ER that makes Udyr spam skills like a crazy ***** XD he has many flexible skill sequences that can mix depending of of the laners junglers etc. BTW this is my first time makigna guide so please don't judge this ****py guide.