As far as I'm concerned, there is only one correct way to play Unclean Beast.

Spit and run. Spit and run.

I see people going for armor/hp items, maxing out ooze, trying to melee other demigods at full heath, etc.

All wrong man. All wrong. Seriously, if you are not maxing out Venom Spit and stacking +speed items, then you should go play an easier demigod, like rook or regulus.

Here is how the game transpires:

Starting off, buy the anklets for +speed, then buy the first helm for +mana and two teleport scrolls. Then port to the farthest tower and go cap a flag. Sooner or later an enemy DG will come. Spit on them. Since they're level 1, at this point they'll probably turn tail and run. Let them run. Kill the creeps. You'll be level 2. Put that point into inner beast for more +speed.

Do this until you hit level 4. It will be pretty easy. Spit on a demigod WHENEVER you see one, but don't chase them too far. If they come to you, just run and then spit again if they are still following by the time the cooldown is up. They WILL run now, because they're almost out of hp. Try to catch them, but again, no sweat. Your main goal here is to harass the hell out of them and not let them gain any exp from creep kills while you do. Make them avoid you.

At this point, if you have been doing it right, and they are not really really good (in my experience 90% of players aren't), then you'll be level 4 and they'll be level 2 or 3. This actually gives you a massive advantage because at level 4 you get the second rank of spit, which is a HUGE upgrade. Now teleport back to base, buy the 10% speed boots, and go back to the lane. Now you're VERY fast. Not only that, your spit hurts a lot. Two spits should get a demigod down to 25%.

What you do: let them push all the way to your towers, then run in, spit on them, and start chasing them. You'll be faster, and you'll be hitting them while they run. When they reach their towers, instead of running in with them, spit again and go back to your lane. The DoT will kill them (it does about 85% of the time, unless they heal themselves, or shield if they're oak (but that's rare because they've already used shield most likely)).

Get the corpose explosion skill (forget what it's called) at level 5. Continue to kill creeps (will be much easier now, you'll be killing 4-5 at a time).

At this point you'll probably be level 6 or so. Keep going for inner beast, and put the other point into either +stats, or foul grasp if you prefer a more aggressive style. I like foul grasp because of the interrupt, obviously, but +stats allows you to be a better killing machine.

I would say that about 75% of the time, one or both of the enemy demigods have quit by the time I hit level 10. This is either because I kill them too many times, or they realize they are not leveling fast enough to keep up. If they haven't quit, then they will soon because I already have mageslayer.

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The most common mistake by far is to go for weapon damage right off the bat. This is wrong because UB has low armor and health, so while you'll dish out damage, you'll also take a lot of damage. And if you're not fast enough, you'll die.

Second most common mistake is to use spit only occasionally. I use it every chance I get, either on enemy demigods or on structures. It's actually fantastic for taking down towers because you do at least 1k dmg and you get hit only once if you're quick enough. But anyway, either get heart of life (my choice), or enough +mana items so that your mana is always full. Spit on enemy demigods as much as you can. Even if they don't die, they'll get low on health and play a lot less aggressively, which means you have more room for doing whatever you want to do.

Another common mistake is a lot of people get bestial wrath. It is a waste of a skill and not very good even when it seems like the time is right (i.e. right before a confrontation). It has a 1 second cast time, has a distinct sound and animation so most people will simply get out of melee range. By the time you catch them, you'll have only a few seconds left on it. I only put points into it in later levels when I've maxed out spit, inner beast, and stats.

Bottom line: play to your strengths. UB is all about speed and damage over time. Don't try to get too creative with it. You may have some success against noobs, but better players will kick your arse.