Top Udyr is usually at his best on the Phoenix lane-control line—Doran’s Ring, R start, and often an early RWR—because that version keeps the wave and the opponent burning at the same time instead of signing up for Blade/Q fistfights.
A very Udyr top habit is to let R start the contact, use W to make the return trade inefficient, and only spend E once they show how they want to leave, so your movement speed is deciding the end of the exchange instead of announcing the start of it.
In real fights, think less about diving past bodies and more about trapping one body inside your stances: awakened R is the usual call when several people or a corridor are involved, while awakened W is the aggressive answer when surviving the first burst is what lets Udyr keep sticking.
Use awakened W when the enemy has finally committed enough damage that surviving the next few seconds decides whether you stay glued to the fight. In lane, that usually means after your R has already started the trade and they answer with the spell or burst window that would normally force you off. In skirmishes, it is strongest when stepping into two people would be correct if you can live through the first hit. If nobody can really threaten you and the fight is about trapping space, awakened R is usually better. If you are guessing before they spend anything, you are often pressing it too early.
Udyr has four basic Abilities that swap between Stances and can Recast an Ability to renew it with Ultimate benefits. Additionally, after using an Ability, Udyr's next two Attacks gain Attack Speed.
Udyr gains attack speed and his next two attacks deal bonus physical damage. Recast: Gain even more attack speed, and the next two attacks call lightning to strike the target.
Udyr gains a shield and his next two attacks heal him. Recast: Gain an even bigger shield and heal based on max health over the next couple seconds.
Udyr gains movement speed and his first attack against each target will Stun them. Recast: Gain even more movement speed and immunity to immobilizing effects for a couple seconds.
Udyr surrounds himself in a glacial storm, damaging and slowing nearby enemies. Recast: Empower and unleash the storm, causing it to track enemies and deal additional damage.