Been playing a lot of on-hit toprianna recently (50k mastery points worth in less than 1 month) and been pulling a near 70% winrate with it in my ELO (silver 2). Just thought I'd share the build since some people have been asking for it. I will flesh the guide section out as I continue to climb with it (can't be bothered to have 9 of 10 lobbys dodged in placements)

IN GENERAL

+ Amazing lategame DPS + Safe laning phase + Extremely good 1v1 + Counters meta quite nicely + Quite durable + Self-sufficient

- Prone to get camped - Vulnerable to burst - Has some VERY bad matchups - Needs items - Short range - Low waveclear

IN RELATION TO STANDARD ORIANNA

+ Scales MUCH better + Can splitpush as well as teamfight + Isn't locked to use spells for damage + Build is far more flexible + Off meta

- Almost purely DPS - Much riskier - Lower damage in teamfights - Selfish - Off meta

Orianna is usually a mage champion that stays way far away from the action, and strives to catch as many people as possible, preferably from the backline, and erase them or at the very least force them out of the fight right away. Which is a valid approach. In this guide, I am in no moment asserting that standard mid Orianna is bad, flawed, or dysfunctional in any way, that would be just lying as that gameplan can be quite effective.

So, let's get this out of the way: on-hit Orianna doesn't strive to do the same job as her mage self in the midlane. Yes, she is considerably worse at catching multiple people out, or following up an engage, but that's not the main boon to building her on-hit. Rather, she is much, MUCH more self-sufficient, much stronger in the side lanes as a result, and as a bonus, since her damage doesn't rely solely on her spells, she is free to use them purely for utility. She essentially is a marksman that always brings her own support to the battle. And, if push comes to shove, she still can do most of what standard Orianna does, such as following engages and setting up AoE wombos, just with somewhat lackluster damage.

She does have a catch after all

This is not to say she doesn't have her weaknesses, but they aren't so severe as to be insurmountable.