Starter Items (for jungle)
I will explain why you would need these starter items for jungle:
Cloth Armor - As I have already explained, udyr needs a lot of armor, also with this Cloth Armor you can achieve killing the golem and end up with more health than you would without it.
5 Health Potions - Even with Cloth armor, without any health potions, and you can't even kill the golem without dying.
I chose these and put them in a particular order because the following:
Maldred's Razors - I chose this item because it builds up to Maldred's BloodRazors, but mostly because of when I chose this item (order). I chose Maldred's Razors in that order is because of by the time you have got that item in that order, you will be occasionally doing ganks and jungle. The reason for the ganks is that Maldred's Razors improve your ganking process,,and the reason for jungle is that Maldred's Razors passive deals over 400 damage to a minion or a monster by a 20% radius.
Boots of Speed - As normal build, there are other items that should be bought before buying a lesser item at the shop, and that is this situation because Udyr seriously needs Maldred's BloodRazors. So it's better to have fully enchanted boots after you have bought Maldred's BloodRazors.
Phage - As a normal Off Tank-AD Melee Jungler, some what needs an item that can slow enemies for a 110% faster and perfect gank. Phage has that passive, but so does phage's full item the Frozen Mallet. So why shouldn't we buy frozen mallet where phage is intended to be bought, I will tell you. As I have already explained ''As normal build, there are other items that should not be bought before buying a lesser item at the shop'', and by the time that you would have bought Phage as intended. You would be ganking all the time, but phage would help decrease your ganks rating of the enemy getting away.
Vampiric Septer - Now udyr needs a ton of damage and life steal and that is where The Bloodthister comes in but it will have to wait because other items have to be bought, but you need a bit of life steal as a low level, so that is why you should buy Vampiric Septer at a the convenient order that I put it in.
Stinger - Udyr needs a lot of attack speed but as I said before there are over items that should be bought, so you should buy stinger before wasting you time trying to buy baron nashor's tooth.
Full End Items
So the explanations:
Maldred's BloodRazors - Increasing Udyr's attack speed, and giving udyr a bonus damage passive
Mercury's Treads - Giving Udyr an equal magic resist to armor, and he needs movement speed to help his third ability (bear stance).
Frozen Mallet - Giving Udyr a Unique passive (every time you hit an enemy, the enemy's movement speed slows for a short amount of time), plus the health.
Maw Of Malmortius - For the damage output and the two uniqur passives
Nashor's Tooth - For the attack speed and the ability to support Tiger stance, Turtle stance and Eagle stance
The Bloodthirster - For The Damage and the life steal, mostly to support tiger stance.