Ao Kuang's The Power, The Rings, and The Heals

One consideration when making your builds, don't commit so heavily into lifesteal. You've got 3 items...at max, you should probably only have 2, and even then it depends. Polynomicon is less for the lifesteal and more for the burst damage after ability use, while Spear of the Magus is a team-based lifesteal option (due to the damage increase for anyone attacking your target). Bancroft's Claw can be paired with Typhon's Fang, but for Ao, I'd probably choose Nimble over Claw. I would definitely not have Poly + Bancroft + Magus in the same build.

Warlock's Staff is usually more for gods in Mid, people that need to box some due to their kit, but Ao is more of an assassin, get in, deal damage, get out. Not sure why you're choosing Warlock here.

I guess in a way there's some synergy though. You have 30% pen via Magus, Warlock and Tahuti. You've got burst damage function from Poly, Archmage, and Claw. It's just not how I would probably play him, esp not in a non-Conquest role. Definitely important to identify the mode / role you intend for your builds though, and info on how you suggest playing for the build would be good to see the strats behind the concept.

For the Rings build, same concept probably on lifesteal. If you're going Bancroft, you probably don't need Telk. Choose one or the other. Depending on how things go, you also might skip over Hastened though I see the appeal. You might instead get a higher power item either for Telk or Hastened, as he really doesn't need that much AS probably. You could also sell Manikin late-game as it's not all that great of an item.

I would personally just completely delete that Heals build. No offense but it's pretty awful.