First of all of you must know that this build is just for fun, and it can be a little bit stupid, but it works perfectly. But dont try it on ranked games because Ap varus isn't good enough for tryhards, one reason is because Varus has a low defensive stats so its a easy target against bruisers.

Ap varus is expecially a late game champion. Since W and R are the only spells that stack with Ability power, this spells will be the main scource of varus's damage. Other spells will be necessary too, not for damage but to "explode" his w spell stacked on the enemy.

Spells strengths:
- In the early game, this spell will not able to do so much damage but its too strong in the late game, lets see why. First of all, spell's passive does Basic damage 10/14/18/22/26 + 0.25 per ability power, so stacking with nashor's tooth it will help farming well and also do extra damage per hit. Now the second ability its weak on early game, but in the late games does huge damage, each hit on the oppenent will stack 1 Blight , up to 3 Blight (3 hits), each Blight does 2/2.75/3.5/4.25/5 + 2% total ability power. In the late game 3 Blights will do 45%+, it's a huge damage even for a tanky guy. Thats why Nashor's Tooth is the most importante item in this build, because it gives you attack speed to apply 3 Blights faster as you can, cooldown reduction to give you the other spells to explode them, and an fantastic passive doing extra damage per hit.
- Fantastic spell, 2 seconds root plus 150/250/350 + 1.0 per ability power , so if u get 600 ability power in the end, ultimade will do 950 magic damage,and in the description says "The corruptions then spreads towards nearby uninfected enemy champions, applying the same damage and immobilize if it reaches them", if you does ulti in a close teamfights it does 950 and 2 sec. root to everyone. Also if u stack 3 Blights then using ultimate, it will do 45%+ plus 950 magic damage.

As I said, this build is just for fun, dont try it on rankeds. Also I wanna apologize for my bad "engrish" I hope you guys can still understand what I meant to say.
I can't tell you exactly the weakness of this build, I only can say that he normally is bad against burst damage and gapclosers(Zed for example) because of his low defensive stats, but when is well played it's able to survive.
So, have fun...