The healing potential granted by Essence Theft is at its best when used with Orb of Deception, as it deals a very decent amount of damage and can hit the largest number of targets.
Against a single target, however, Fox-Fire will return more health, since each of its fires are single-target spells which gain the full effect from spell vamp. This is assuming the target has relatively low magic resistance.
Consider leveling Orb of Deception and Fox-Fire over Charm; this will make you a primary source of damage mid-game, although the lower CC time is a noticable loss.
Initiating with Charm will allow you to maximize your damage, as the target will be unable to dodge Orb of Deception and they will take the brunt of Fox-Fire's damage.
Orb of Deception is a boomerang skillshot, meaning you can move after casting and it will change the path of the orb as it comes back. Spirit Rush can help you to lead the orb's return.
If you hit an enemy with Charm and then leave its area of vision, for example, by walking into a brush, it will no longer follow you until you get into its sight again. The slow persists in any case.
Though Spirit Rush itself is only one spell, each dash will reset the cap of Essence Theft, making it possible to gain up to 9 charges with it.
In the early game, Spirit Rush is great for finishing off running champions as you can usually turret dive safely since the skill can be used three times before going on cooldown.
It is best to save the last spirit rush for escaping from turret range if it is used for turret diving.
Using Spirit Rush all at once may not be the smartest choice in a fight. Try saving them using them to position yourself for your skillshots, chase down stragglers, run away, or to turn the fight with another quick burst to the right champions.
Spirit Rush's cooldown is fairly reasonable, and will be available in most team fights. It is also great for escaping, as it can also be used to jump through thin walls.
Abyssal Scepter helps Ahri greatly as she will be close to the enemy team in many fights, however; since the nerf on Abyssal Scepter's range, it's magic resist aura may be less consistent, as many of her spell's range exceeds the 700 range aura.
Since Spirit Rush's Essence Bolt range is the same as Ahri's auto-attack range, she can deal high amount of burst by dashing towards an enemy and immediately auto-attacking them to proc Lich Bane's passive without getting into melee range.
All of Ahri's spells can be avoided with proper positioning or juking. Her Orb of Deception and Charm spells are line skill shots that move fairly slowly so you can step to the side to avoid them. Her Fox-Fire and Spirit Rush spells target the 3 closest enemy targets, but do prioritize champions in a smaller range, staying behind minions, tanks, or your team can help you avoid some or all of the damage or make Ahri risk putting herself in a bad position if she wants to damage you with them.
Buying health can help you to survive against her true damage.
Always remember to move away from her Orb of Deception path after she uses the spell as the orb will return to her and deals true damage to you.
Take cover behind minions when engaging her in order to avoid her Charm.
When Ahri uses her Fox-Fire, take cover behind minions so the spell will only hit you once.