Though Warwick's strategy may vary from one to another, he is an excellent jungler and a powerful solo laner.
Many of the Warwick strategies can be used at any Summoner level and do not require specific runes most of the time. However, without decent runes and masteries, he is quite slow and is bound to lag behind even if it's possible to clear the jungle without dying.
If you want to jungle well on Warwick it is recommended to use runes giving attack speed to maximize the health regeneration from Eternal ThirstEternal Thirst as well as increasing his speed as well as using armor runes to minimize monster damage, especially at earlier levels.
Many of the same strengths which help Warwick jungle well helps him solo lane efficiently against many champions. Due to his Hungering StrikeHungering Strike dealing a large chunk of damage as well as healing Warwick he can easily pressure his opponent while remaining at high health.
Hunters CallHunters Call can help a lot when pushing a lane since it will increase the attack speed of both you and your allies.
Turn Blood ScentBlood Scent off to fool weakened enemies into thinking that you are not nearby, but don't forget to turn it on again later.
Warwick excels at hunting down fleeing or weakened enemy champions after teamfights. At max level, Blood ScentBlood Scent reveals the location of enemy champs with less then 50% health from great distances and gives him a large boost in speed for chasing, it also reveals their locations for all friendly champs, making escapes very difficult while also preventing bush jukes.
Warwick is also very useful in killing his pursuers. While running, cast Infinite DuressInfinite Duress to regain most of the health you have lost, then spam the rest of your skills. This should shut down your pursuer's hope in killing you.
Casting Infinite DuressInfinite Duress on the enemy carry is the priority for Warwick in any team fight. The cooldown on the skill is relatively short, so don't be afraid to use it if you think it will grant your team a kill.
Infinite DuressInfinite Duress is easily disrupted by a stun, knock-up or suppression, so wait for the enemy disables to be used before using this ability.
Madred's Bloodrazor has a great synergy with his ultimate, but due to its high price and as most players choose to build tanky before going for damage, it is recommended that it should be bought as a fourth or maybe fifth item.
Building some survivability is crucial for Warwick since he has no innate defense mechanisms as a melee champion.
By building him tankier, Warwick becomes incredibly hard to kill due to high healing while still being able to put out hefty damage on enemies without having to fear sudden death. This will also maximize the effectiveness of any proc items you get by allowing him to stay in the fray for longer.
Warwick's lack of any multiple-target or AoE damage means he may miss out on assists during a team fight. Ionic Spark ensures Warwick does some damage to nearby enemies when attacking, allowing for assist credit. Buffing friendly champions with Hunter's CallHunter's Call will also provide assist credit.
Jungling order: Blue Golem (smite) → Wolves → Wraiths → Red Lizard (smite) → Small Golems → (Fountain / Gank) → Wolves → Wraiths → Small Golems → Wolves → Blue Golem → Wraiths → Red Lizard → (Gank) → Fountain at lv 7 → Dragon (assumes having Madred's Razors)
Note: another set of starting items could be Cloth Armor, 2xHealth Potion, Sight Ward. The ward is almost always used to ward your own Blue Golem or Dragon, so if an enemy jungler attempts to take it, you can set up a gank. Alternatively, you can place the ward at enemy Blue/Red to try to gank the enemy champion trying to obtain the buff. Use Hunters CallHunters Call after the 2nd attack in order to gain the most healing efficiency with Eternal ThirstEternal Thirst.
Once he builds enough attack speed and life steal, Warwick can largely sustain himself simply by attacking, Getting Thornmail will cause him to take 30% of his dealt attack damage reducing a portion of his sustainability.