Updated Orianna DPS build - 1v9 SoloChad Build
I've only ever ran this build with Conqueror Runes, but I assume proc'ing PTA would be pretty easy with her as well, just depends on your preference.
Runes: Conqueror - Overheal - Alacrity - Cut Down, although Coup de Grace works well too. Manaflow Band - Transcendence, although Celerity or Scorch work well too. 2 AP, 1 Health although you can swap a mag res or armor in to be less squishy early on.
Spells:
Ghost is pretty useful for securing kills as well as exhaust, but ignite works fine as well. Flash is recommended.
Starting Items:

First Back:

Early Game:

Mid game:


Core:

Late Game:

Full Build:

Other Items I run:

Style of play: Outside of the laning phase, you'll likely play more like a botlane-carry than traditional Orianna builds, proc'ing conqueror off of auto-attacking, q and w, which towards the end of the game you can spam without much penalty to your mana bar. Because her passive adds a percentage of AP to her auto, Items with attack speed and ability power are the key component of the kit. I like to run Guinsoo's and Nashor's, although there are a cocktail of items like Wit's End that work. Ori also doesn't have any real engage/disengage aside from her ult and she's not very mobile, so items with an active slow like Gunblade/Iceborn/GLP are pretty useful, although Gunblade works best. This is because Ori is mad squishy, and building defensive items isn't the most efficient for marksmen/mages. Seraph's active shield and Orianna's E make up for this by adding up to about another half-bar of temporary health in shields. This ideally grants enough time to fully proc Conqueror, and with a bit of added lifesteal she has enough sustain to 1v5 since she auto's and q's so much. The only items that offer AP and lifesteal/spell vamp anymore without ravenous hunter are Gunblade and Maw of Malmortious, which allows both offensive and defensive approaches to the build, although I'd recommend Gunblade
As opposed to a more conservative, team-fight oriented Orianna, I like this build because it allows you to play her like a carry, which embodies solo-queue imo.