Muramana is a kinda broken item that also miraculously fixes Warwick’s mana issues. Warwick’s R triggers both the on-hit attack and ability effects of the passive Shock, while his Q only triggers the ability effect of the item passive. So it’s even better on Warwick compared to some other champions.
Divine Sunderer’s Mythic passive gives you pretty much most of the penetration that you need for the build to be efficient.
The build revolves around applying as many on-hit effects as you can and using the way life steal works to heal extra on your Q, R, and on-hit effects. All On-Hit effects in this build benefit from life steal, and all On-Hit effects in this build get applied by your Q and R.

I have an older version of the same build idea but with crit items and Kraken Slayer as the Mythic, however, due to Kraken Slayer not working on melee champions in combination with Guinsoo (Yes, that is a thing), I've scrapped the build due to not dealing as much damage as it would be possible on paper if it worked properly.

Me and Galvan have found out while testing that Warwick’s R being 3 different attack instances in 9 instances of damage is one of the few, if not the only ability in the game that can benefit from the 12% damage bonus of press the attack while triggering press the attack itself. Provided that you trigger press the attack in the 1st or 2nd attack instance, either the 2nd and 3rd or just the 3rd attack instance would benefit from it.

Numbers:

I used practice tool with the following build:
Sorc Boots, Muramana, Divine Sunderer, BotRK, Guinsoo, BT.

Due to practice tool not allowing me to add resistances individually (i can only add +10 armor and mr at once), the build does less damage calculating numbers this way compared to a real-game scenario. Most champions have lower base MR compared to Armor, and MR is harder to itemize for especially if you're a squishy who wants damage.

The Build deals 4298 damage in the AA > AA > R > AA > Q combo and 2064 with a solo R against a target with 2000 HP, 80 Armor and MR, which is a bit tankier than typical for a late game squishy target. Yes, with this build you have enough damage to oneshot any squishy target that isn't ahead of you in levels and items with just one R, which is pretty funny. I have a clip of this happening here.

It deals 3255 damage in the full combo against a target with 4100 HP and 240 Armor and MR, which is about as tanky as a full tank build on average (if not tankier). It deals 1533 with just R.

It deals 3906 damage in the full combo against a target with 3500 HP and 150 Armor and MR, to represent a bruisery build, not too tanky, not too squishy. It deals 1886 with just R.

If you're playing this in the jungle your main goal is to snowball. Since we're not getting Tiamat in order to snowball better our jungle clear will be pretty poor on the red buff side camps, so we're going to be focusing on perma ganking. Even if you just got level two, if you see your W passive activate, and the lane is close to you, go there. At worst, if you play it right, you get away with no takedowns but waste some summoners, assuming the enemy stays. At best, you get a couple of kills and you can continue your jungle clear to back and get tear + sheen at the minimum.

I always start bot side for the better leash. If i am on top side on the map, I do Blue > Gromp > Wolves > Raptors > Scuttle > Red > Optional - Krugs with any ganks i can squeeze in between before i back. If i am on the bot side of the map, I do Red > Raptors > Wolves > Blue > Scuttle > Gromp and any ganks i can squeeze in between before i back.

At this point you should be around level 4-5 and at your first back, ideally you would have enough gold to buy tear and sheen. After this I usually always try to go to drake and solo it, or gank bot for priority and take drake with them. Always buy a control ward if you can afford it, and swap to sweeping lens on the first back, to ensure that you can potentially do drake without being interrupted, and because lens is super useful to gank with in general, so you might as well swap on the first back.

Other than this it is pretty simple, take the easy camps when they respawn, try to permagank, try to take the objectives on respawn.

For top lane, most of the time you play this as a regular Warwick top, really the only difference is your itemization and playstyle later in the game besides the fact that you're looking to stack your tear. However, snowballing still helps a ton, so i recommend roaming to mid / scuttle fights whenever you can and don't risk losing minions.

Also, the nature of this builds allows you to constantly keep fighting, so don't be afraid to do that as long as you understand your damage, you have a lot of healing especially at low hp and this can be very surprising to some opponents that can't instantly burst down more than 30% of your hp at once. I've won fights 1v2 because my opponents underestimated low hp Warwick's sustained damage and healing capabilities, both in top and jungle.

Now, some of you who know me may know what I'm a fighting game player, I quite enjoy labbing, min-maxing and stuff like this. So, here are a few combos/strings that you can do to maximize your damage:

Standard quick high-damage combo, recommended vs duelists and squishy targets:

AA > AA > R > AA > Q > AA and Q loop if necessary

Standard Long Version, recommended vs duelists, bruisers and tanks:

Q > AA > AA > R > AA > Q > AA and Q loop if necessary

Early Game Sheen combo (recommended at low levels when your cooldowns are high, and obligatory, you have sheen):

Q > AA loop > E1 > AA loop > E2 > AA loop > Q > AA loop > W > AA loop > start over if necessary

This string would amount for about 5 sheen procs in 7.5 ~ 8.5 seconds if done perfectly, assuming the fight lasts that long. You use the 2nd E cast right before it is about to run out and you see in your item bar that the cooldown from sheen is done. You can get ingenious hunter if you're feeling cheeky and think that you can do it faster or you prefer a larger margin of error.

*Notes:
Sheen effects does not get duplicated by Guinsoo's phantom hit.
E has two casts, both can trigger Sheen effects.