Okay. For a different set of opinions, because I personally don't like tiger, although I do like its concept.
Currently jungling with Phoenix, an explanation:
First level, take:
Items: Cloth Armor, 5 Potions.
Head to the Golem camp. Position yourself near bottom so that when you attack Golem, your stance will proc, hitting them with the cone and the AoE. Hit your health potion when you get hit by golem. Smite it immediately if you can see all enemies, or if you're playing cautiously, save your Smite until it's at 450 or so. Smite.
Since you have Awareness (+5% EXP) maxed, you should level up once you've killed the minions and Golem.
At this point:
Skill: Phoenix, Turtle
Items: Cloth Armor, 4 Potions.
If you need to pop another health potion, do so. Spam phoenix but try to save some mana if you can. If you're still low on HP, use turtle stance to mop up and gain a bit of HP back. Head over to wraiths. Pop another health potion, phoenix it out. At this point, your smite should be up or almost up, and you should level. (Unless your mid is a fricking ******* and stole some exp. In which case, you're in for a bit of painful jungling. IF YOU'RE A MID WHO EVER DOES THIS, YOU'RE A FRICKING ******.) Head over to double golem camp.
At this point:
Skill: Phoenix, Turtle, (Phoenix/Turtle)
Items: Cloth Armor, 2-3 Potions.
Turtle is much safer than Phoenix to level up, but Phoenix gets the job done much quicker. If you want to get your jungle over with and gtfo to gank, go with Phoenix, but it's a bit more risky. If you want to take your time because all the lanes look cautious and not out of place, go with turtle. If you took turtle, spam that and smite one. You'll actually gain HP, but it'll take you a bit to kill them. If you took Phoenix, take a bit more care to stay out of the way of one of the golems when you start it up. Use another health potion, then head over to lizard.
If you took Phoenix, follow this:
Wait for your potion from double golems to run out, then smite then use another. Go in when you're around 75% health. Start whacking away with phoenix. You want to recall, get boots or a longsword, then head out and gank someone/kill some more jungle minions to get that madred's razor going.
If you took Turtle, follow this:
Spam Turtle, smite it when smite pops up, because you might take a bit. You can probably go kill the wolves, then wraiths/golems again if you feel like it, because they will have probably respawned by now.
In my opinion, Turtle is a lot safer than Phoenix. Running through jungle with Phoenix is when you really want to burn through it, basically, and don't care about your health. You just want to get through it. Turtle is for a slower, more reasonable jungle where you get out at a far more reasonable health.
At this point:
Skill: Phoenix, Turtle, (Phoenix/Turtle), Bear
Items: Cloth Armor, Longsword/Boots, (Or Madred's Razor if you went turtle), 1-2 health potions and/or a ward.
If you can, go gank someone/throw a ward up at dragon. A slow plus your bear stun should ensure you get someone if they're out of place and at decently low HP. Help from your allies gets you that sweet EXP and gold you thrive on. Plus some feed for your allies, of course.
When you're a higher level, and your bear stance has some decent levels, use bear to get around. Especially when you have golem, it gets you a sweet boost from place to place.
Turtle stance infuriates people when you have a good defense against their brand of attacks. They get nearer, which lets you lead into a bear->phoenix combo where you stun them and run by them, allowing your aoe to deal damage.
Stunning a group of people in succession is incredibly amusing.
WHEN RUNNING FROM A MORDE ULT, USE YOUR TURTLE STANCE. Any global ult, for that matter. Udyr can escape from some serious **** with less than a fifteenth of his HP by spamming that shield and hoping for the best while also slamming on Bear stance to run away.