Another thing, though I don't know Ori's AD, or AD per level.. And since you are level 11, with no runes or rune pages.. I'm not 100% it will apply, but I'm going to throw it out there anyways.
Most of the time, if you are pushed under your tower, assuming all your minions aren't focusing the minion, it works like this.
Melee Minion - 2 tower shots, you auto attack once, dead.
Caster minion, attack BEFORE the tower, tower shoots it, you attack it once more, dead.
And I noticed you said you didn't know about cancelling your attack animations, yes, meanwhile I don't think it will benefit an Orianna player much, there are many abilities that if you use immediately after your attack, it resets your animation, usually increasing the speed in which you attack.
There are also many champions that, at high level play, to be used to their full potential require you to move after each attack, because their recovery animation, I guess you could call it, is so long.
Essentially, when you attack, the moment you see the damage numbers pop up, move your character, even if it is just a little, then target the next target, or the same target right after. Practice this and meanwhile, since you are new, you may not notice a huge difference in your attack speed, it is there.
It is most noticeable when chasing enemies, though, again, hard to master, your character moves faster if you run to them, attack them, then move past / along side them, attack again, move, attack, move, attack.
You will get in many more attacks and cover ground quicker using this method.