You're on the right track, but I think your skill build is a bit off.
I go like this.
R > Q > W > E.
Ghost + Teleport
Red: Armor Pen
Yellow: M. Regen/Level
Starting items: Often regrowth pendant + hp pot, but I'm still fiddling with this setup.
The reason you level Q aggressively is for the cooldown reduction. Since he scales so much better off last hits now, it's very much worth it to level Q early and get a glut of last hits as soon as possible. Nasus wins games by farming and spiraling his bonus damage out of control. If you're allowed to free farm for 10 or 15 minutes and can last hit, you should be able to crush the enemy team.
I like W as a secondary skill for two reasons. One, it's useful in lane (particularly if you're solo). You can harass rather well by casting W on someone, running up, smacking them with Q, then backing off before they retaliate. I typically wait until my Q is nice and farmed up before doing this. Most people do not expect levels of burst that strong and it's quite possible to kill someone after a couple iterations of this. In teamfights starting mid game it's quite useful as an anti-carry skill and strong CC to kill a focus target.
His E is not a bad skill, but you should not be casting it indiscriminately in lane. It's there to help you control minion waves, and should only be used if your goal is to push/counter-push the lane. Often, this is not necessary, but if it is then level it up. You might also want to take it there's no attractive target for W.
Item wise you're on the right track, but be mindful in the order you build items. Rushing Sheen's a good idea, it gives you a strong boost in damage and burst while beefing up your mana pool. Rushing Trinity Force is only appropriate if you are doing well and the enemy team's damage output is not a threat. If you're getting focused down or taking too much damage in fights, you should be focusing more heavily on defense oriented items. The standard ones apply here, Randuins, FoN, etc. Rule of thumb is that Nasus does best if he doesn't die. The longer he lives, the more damage his ult does.
I find GA effective on him for two reasons. For one, Nasus coming back up can still deal a vicious amount of burst damage with his Q and often score a kill on the stragglers waiting to pick him off. Secondly, GA is often a focus deterrent. People will be unwilling to spend the effort on bringing someone down with a GA and focus instead on other targets. This can work to your advantage by allowing Nasus to wreak havoc unmolested amongst the enemy, but might also backfire if you need to be a damage sponge for the team. Again, it's a good item if you're already doing well.
Try to get into a lane where you can get a lot of last hits and farm up that Q. Interestingly, while Nasus benefits greatly from a solo lane, he's not the strongest solo champ ever in my experience. Ranged champions can harass him pretty hard, and that can be very hard to deal with. His options for retaliation are limited, and the lifesteal from his attacks may not be sufficient to keep him up. If you can go against a weaker solo, do so and focus heavily on farming. If you simply can't deal with them, there's no shame in going into a duo lane. Better to get some last hits than none.