Udyr has an ability for everything. That is why he has no ultimate. Nothing goes to waste on him and the reason he has no real gapcloser is because his Bear Stance gives him a LOT of movement speed and extends his basic attacks range extremely slightly for the stun attack. If Udyr got a gap closer, he would be uncatchable. It would also really not fit in with his kit since he is more about enhanced basic attacks and basic attack effects than anything. Also, he has 4 abilities that equal an ultimate and more truely.
Tiger Stance- Biggest AD Burst in the game. It causes your next basic attack to deal up to 230 (+160% AD) physical damage over 2 seconds and then 115% of your attack damage from the persistent effect and the basic attack. Not stopping there, it also gives a pretty decent attack speed boost for a moderate duration that stacks with his passive for a lot of damage.
Turtle Stance- A spammy shield that also gives him a lot of lifesteal ever since the overall lifesteal nerf. Effectively, with some ability power, Udyr becomes a super tank with sustain with this ability. The ability power also benefits his Pheonix Stance as well and the lifesteal makes him an extreme wall during the laning phase if you choose to lane Udyr. It also provides him with his jungle sustain.
Bear Stance- Udyr's butter on toast, Bear Stance allows Udyr to gain an extremely large movement speed boost for a decent duration and adds a stun to his first basic attack that has a decently short immunity time in a chase or extended duel. It's so simple yet so satisfying.
Pheonix Stance- This is the main reason Udyr is known for his wave clear. Every third basic attack he unleashes a cone of fire that deals damage equivalent to a spell cast that can be done multiple times. Not only that, it also causes rings of flame to be unleashed from Udyr around him to quickly deal damage to enemies around Udyr, dealing once again, a lot of damage.
Udyr can then combo these abilities together to stack his passive to give him bonus movement and attack speed. He can start with a Turtle Stance to block the initial burst before switching to Bear Stance to run in and perform the stun on his opponent. Then he can activate Tiger Form to apply the damage over time and gain the attack speed while also applying some increased damage basic attacks while he waits for the 2 second global cool down. He can then activate Phenoix Form to make use of his huge attack speed boost from his passive and Tiger Stance (100% boost at Tiger Level 5) to further increase the amount of fire cones he can create with his Phenoix Stance. The bonus movement speed from Monkey's Agility also allows him to keep in range of his enemy to deal damage with his rings of fire. This amounts to a huge amount of damage when combined with some items like Trinity Force and Wit's End.
(also, it is impossible to ward off every single gank route for a jungler, there will always be a way too gank an enemy)
