Honestly a lot of the viability of an Udyr pick depends on how well you can predict skillshots and movements to your advantage. I've honestly had times where i can pick Udyr into hard counters like Lux or Zyra, and been fine. If you have unpredictable movements, predict their skillshots, and manage to get the stun on them, you can pick Udyr in tiger or phoenix into just about every team. Some things you should be aware of are things like Anivia, sometimes Nautilus (but you shouldnt let a Nautilus even get the pleasure of ganking or having buffs past 2:20 IMO). One more pick to never go into is blue Ezreal, and sometimes Jayce. I feel more inclined to pick Udyr if my team gets Jayce though, as he allows me to do whatever the hell i want. Ahri can also be a tough pick to face if you dont gib her hard.
Honestly the most important thing about Udyr is how you teamfight him, IMHO you should just play like an adc, attack whats in front of you and deal as much damage as you possibly can. Running through 4 other players to kill a backliner is always risky, especially if you're behind and have no hard cc for their backline apart from your own.
IMO At first, you should learn your limits with the champion, pick him when available, and learn your limits. Experiment with item builds, routes, counterjungling, and find a rhythm and a mindset with the champ which works for your playstyle. Don't just stick to Phoenix and then maxing turtle second, try Tiger, max bear 2nd, or Phoenix and maxing bear 2nd. Find your limits with Udyr and you'll get increasingly comfortable. I always max bear 2nd for mobility, and the increased ability to stick to targets. But just don't limit yourself whilst learning Udyr :P