You're gonna want to start Blue, as Ornn is VERY mana dependent. Not so much as someone like Olaf, but still very very much so. From there, go Gromp, Wolves, Chickens. Then Skuttle if you can. By this time you should be level 3 and can look for a gank. After your gank, go to your Krugs and then Red. You can then look for another gank as you make your way back towards gromp and wolves as they will be respawned by this time. After that, your chickens, then blue, so on and so forth.

Ornn's greatest strength as a jungler without a doubt is that, if played right, you never have to recall. Because Ornn can build himself items, the only time you'd really NEED to recall is to top off pots/health and mana. With Blue and Red buffs as well as smite, you don't really need to worry about any of this!

Try to maximize your extra map pressure by beating out your opposing jungler to vision spots and drag/herald in the early game. Since you don't have to recall, you'll scale faster than they will too. Which means you can start to apply your pressure faster and harder than they can.

Once you reach level 6, you're going to want to try to gank every time your Ult is up. It's an absolutely AMAZING setup tool, especially for lane ganks. Be on top of vision so they don't see you coming and you'll almost always guarantee a flash/kill.

Late game, group with your team and look to force teamfights. With your insane resistances and health, You'll almost always be able to just run the enemy team down with how little they can touch you. Keep a watchful eye on your carries and peel for them if needed.