I came up with a really crazy build for Nasus and went to test it. I was surprised because that build is very OP. I managed to carry games with bad matchups, horrible teams and even myself doing some mistakes. With any other champion, in a situation like this, I would think: "I lost". But even with all that, with this build I could literally do 1v9, because the focus in mid to late game is totally on taking turrets and the enemy nexus.
And it's somewhat similar to Inting Sion Strategy, but better, because you are a ****ing Nasus dealing 1.5 to 2k damage to turrets by Q, a demonic wave clear and a amazing 1v1/1v2. It's all that a perfect split pusher will need.
And in the late game, while most spliters are forced to team up with their team (and when the standard Nasus loses a lot of strength), you can do almost 600-700 of damage per Q on the tower WITHOUT MINIONS (if you have 1000 stacks and full build). You'll be able to play as an inting sion and put a lot of pressure on their base just by being alive and not appearing on the minimap.

Not to mention the benefits for early and mid game: you'll have a amazing wave clear for split mid game (what's game changer, believe me) and if the matchup it's not good, the E first or E max strategy will be much more powerfull and viable because of the bonus ap, so your lane phase will not be undefeatable or a stalemate, independent of the matchup.
Furthermore, you won't lose much in resistence, as the build has plenty of health, armor, and magic resistance. With your ult, you will have 4k of heath, 240+ of armor and magic resist. That's as much or more tanky than many bruisers building tank items. And with phase rush plus all rune, item and ghost move speed bonuses (plus tenacity) you'll have a lot of mobility and will be hard to kite.

PROS

Super easy champion
Good to learn macro
Scales super well
Super amazing split pusher
Super amazing duelist
Can do 1v9 only with good decision making
Super slown ability
Sustain and life steal
He is a bruiser: a tank with a lot of damage that destroy assassins
He has a amazing wave clear (with this build)
He is the perfect split pusher: amazing tower damage, wave clear and duelist (with this build)
He is the perfect flex lane phaser post lvl 6: amazing sustain, poke and all-in (with this build)

CONS

The weakest early game of the LoL
Mobility for engage and disengage is super dependent on items, runes and spells
Mana is super dependent on items or runes
No means to walk through walls (easy to ambush or escape of Nasus in jungle)
Struggles against true damage and hard CC

Core

Lich Bane

It's the best ap item for Nasus. It has the Shen passive but with a differential. It procs in towers. And with a full build the bonus damage is huge.
Also you gain ap, ability haste and movement speed: all good for Nasus.

Hullbreaker

Best split push item ever, it'll give you a lot of armor, magic resist and hp. Also, you'll get 20% bonus damage to towers and enchanted minions (witch is huge, because no mage will can stop your minions from reaching the tower). The only downside is not being able to stay with your team for anything else. The good side is that focuses you in one objective.

Mythic

Night Harvester

This is the best mythic available. You get more ability power and hp (witch is great, because that matches with the core items). But the essential part is that you get a lot of ability haste. Nasus need it because of Q cooldown.

Last Items

Rabadon + Void Staff

It's the standard build for much more damage in towers. I ONLY CHANGE THAT if there's a enemy champion that can win 1v1 against me and I need to revert that situation to get to the towers. I recommend to change Void Staff if three or more enemies are squish. If not, change the Rabadon.

Zhonya's Hourglass

To use against physical damage champions. The ability haste of Zhonia allows you to combo that item with Plated Steelcaps losing only few 10 ability haste.

Banshee's Veil

To use against ability power champions. The ability haste of Banshee allows you to combo that item with Mercury's Treads losing only few 10 ability haste.

Shadowflame

To use against strong shield dependent champions. It also gives you a lot of ability power and hp

Morellonomicon

To use against strong heal dependent champions. It also gives you a lot of ability power and hp

Read notes of "ability order" section, please.

Your focus is to play safe until lvl 6. Your only objective is to farm.

If the matchup is something you already know how to handle, Q max.
If not, E first.
If it's a hard matchup where you don't have kill pressure, E max.

With Q max

your objectives are:
-to farm
-to stack
-to all-in on enemy to snowball
-and not be ganked

How to all-in?

First - never fight at a disadvantage. Do not fight at high level, item or spell depletion;
Second - wait for enemy utilize a important spell (usually some kind of dash, because without that they can't cait you), you can force that utilizing your W on them and waiting for cooldown (often their dash has a higher cooldown than your W). Or just wait for the enemy to get closer than he should;
Third - do not reveal your intentions through your movement, go at once utilizing the surprise and the right time (just don't do it if you need him to spend a skill the wrong way, or you risk wasting your ghost and ult for nothing).

With E first

your objective is to survive and farm. Focus on stacks only after lvl 6. The remainder is equal to the Q max strategy.

With E max

your objective is only to farm, each stack is profit. After lvl 6 your objective will include poking too, until your enemy needs to go base and you can take tower.
For that let him push (so you don't get ganked) and start poking. When he has half his health, start pushing him under his tower. Poke him under the tower and he will have to go base. Take the turret (at this time I ult, because usually I don't have kill pressure, so it doesn't matter, better take the turret faster).

If it's still before 20 minutes, push top and go herald (if your jg can help, ideally) or split (taking the second tower of the top).
If it is after 20 minutes, just go bot and begins to split.

For split correctly you need to:

First: look at minimap and see where enemy champions are. Of the enemies I don't see, if I have them in my lane, can I kill them? If yes, split. If not, just do another play (usually I push the wave, I stay hidden for a possible pick off and wait for them to show up);
Second: always split on the opposite side of an important objective, and when you do that, push the wave about 1 to 2 minutes earlier (so you can have time to see enemy reaction: who came to stop the wave's clash? where are the others? Are they going towards the objective or are they waiting for me?);
Third: near of their tower, poke squishes, duel weaker imobile enemies and if there is a too strong or to mobile enemy, ult and destroy the tower (like inting sion).
Fourth: never start a split push with all your teammates dead. Your tower are your priority too, defend them.

Bonus Tip: in mid game, pick off enemy champions with gold rewards is a good way to get feeded or get your team back in the game. Save your spells and abilities for enemies with rewards.

Teaming up is not an option, so keep splitting. If you are very strong, with a lot of stacks and items, you can start taking towers even without minions.
If they have inibitor and nexus towers open, play like a inting sion. It's usually worth it to kill yourself to get Nexus towers, but do that in the correct time. Only your presence can stop them from going baron or dragon. But if they go baron or dragon, you should go their base, even without minions.
Communication with the team is key, tell them when to defend and when to press certain goals so you can make these plays. Play with intelligence and don't spot yourself in minimap without thinking in consequences.

10 minutes

Minimum - 100 stacks
Normal - 150 stacks
Excellent - 200 stacks
Perfect - 250 stacks

20 minutes

Minimum - 300 stacks
Normal - 350 stacks
Excellent - 400 stacks
Perfect - 600 stacks

30 minutes

Minimum - 700 stacks
Normal - 800 stacks
Excellent - 900 stacks
Perfect - +1k stacks

44 minutes

Minimum - +1k stacks
Normal - 1.3k stacks
Excellent - 1.5k stacks
Perfect - 2k stacks