Soldiers don't have an AD ratio and do not proc on-hits.
On-hit is a secondary benefit of an auto attack. Something that reliably occurs as a part of an auto-attack.
On-effect is actually "On-attack" that you're thinking of it. It is an ability that is applied by the auto attack action itself...not with the auto-attack.
Generally, on-attacks are applied by the next auto attack, while on-hits are applied on every auto attack, some with a windowed or 'stack' effect.
Jax's R is an on-hit; every attack applies a stack, with every 3rd procing it. Jax's W is an on-attack effect. It is applied by his next auto-attack action.
Cho's E is an on-attack option. It is applied by every auto attack, not 'with' it. You can visually see this in Cho'Gath's case. E applies after every auto attack, though it is probably the largest exception in the game when it comes to on-hit/on-attack rulings since it applies to every auto attack.
In all cases, on-attack effects are considered abilities, while on-hits are not.
In Azir's case, his soldiers replace his auto-attacks if they are in range. They do not carry the normal benefits of auto attacks. They do not even count as auto attacks. They count as spells, and are not even on-attack. They are simply spells that replace his auto-attack entirely.
would work on Azir 
. I know that it triggers on-hit and on-action actions but how would that work with Azir? Would soldiers also be triggered with Guinsoo's rage? Also let's add in Nashor's tooth. Is it possible it would affect the soldiers with the combination of the two? Can someone explain to me on-hit and on-action effects? I mean I looked it up but I am still vague on exactly how it works, especially with Azir. Thanks.
