So Warwick Q has 100% AP scaling. When fully maxed, your Q also heals you for 90% of the damage it does. That means if you do 400 damage with your Q, it heals you for 360, (without any of the extra runes or omnivamp buffs which you will be running). The ability actually does decent damage but it also heals you like crazy. More importantly it is on about a ~5 second cooldown for most of the game.

The main rune doesn't really matter that much but the two important things are presence of mind and ravenous hunter (or one of them can be replaced with revitalize but I don't think its as good). Most games your Bloodline will heal you for about 1k health by the end and ravenous hunter 3-5k. I personally take electrocute because you can auto-Q-auto and they can't do much about it because you leap to them when you Q.

Any AP items work on Warwick but the new Riftmaker item works really well. You get 15% bonus damage after 5 seconds in combat and then it becomes true damage. As you are essentially playing giga sustain you will be in combat for 5 seconds most of the time. If you are playing into someone like leblanc who can just kite you, I would take rocketbelt because you get a damaging dash and then extra movement speed towards them. Nashors is also the other item that I would also take as the on hit works on your R and its kinda just busted.

I would decide whether or not you can trade in lane and if its a yes i.e. its a melee match up, I would go for auto-Q-auto trades. You don't really want extended trades early because your Q is on a long cooldown and your mana is pretty small.

Once you get your mythic I would start going for kills (you can earlier if they are bad or jungle is ganking)

Warwick mid is especially potent at roaming. His W allows him to get movement speed towards low health enemies. Early game you get enough movement speed to out roam every opponent. So when I see the W activated, I will normally try to go for the roam unless I am pushed up, as Warwick isn't that strong late so you want your team ahead.

Honestly, Warwick's team fights aren't the best however AP Warwick is a bit stronger just because he can heal like crazy if he has enough ability cooldown. I would still R their carry and then kill them. After that I would try to Q their bruiser or tank because of the percentage max health damage on your Q so you will heal back more health.

The two categories of matchups are:
Can kite you / ranged AP = you're fcked
Melee / Assassins = you win