Irelia should be played as an assasin and an assasin only.She has unique skills that in my opinion support the assasin role.I Have tried building her as a tank and as an ap burst but trust me the build you will use have given me the best games i could possibly get with her

For summoner spells i consider GHOST as the best choice for her and then the most times i pick ignite!
Secondary is GHOST AND flash or Ghost and Exhaust
Rest is useless!

The runes i use for irelia are Armor penetration marks and quintessences and mana regenaration glyphs and seals for my bladesurge farm!

Start with a dorans blade and head top or mid.As soon as you have farmed 1600 gold go back and purchase sheen and boots.Continue farming and finish your trinity force with this order
Sheen-phage-zeal
Once you have trinity force you should be an unstopable force with a good start.
You should be focusing on building your next item which should be Youmus ghostblade and its the perfect item since you will be upgrading your wuju style by those lvls and it procs great with wuju style for more extra true dmg.
After building youumus you can start building your starks fervor for some lifesteal and attack speed making you a beast on 1vs1 situations
Last in my opinions sword of divine is a perfect item for her since you will have armor penetration runes and this item will give you a pretty decent amount of damage against tanks with huge armor
Lastly guardian angel for being able to keep your killing sprees alive!

Pros
1)Great farm
2)Great assasin
3)Great 1VS1 duelist
4)Good health regen even without lifesteal(cause of wuju style)
5)Not team dependant
6)Good cc
Cons
1)Squishy
2)No farm=useless
3)She needs kills!
4)Not the best jungler!

First of all irelia can jungle
Althought everyone thinks that cause of her Wuju style it can be pretty easy i must say that her jungling isnt the best role for her
Because i know most of you will want to jungle with her i will Explain how i jungle effectivly
IRELIAS JUNGLE IS DEPENDENT OF RUNES IF YOU DONT HAVE THE EXACT RUNES DONT JUNGLE WITH HER
ATTACK SPEED -MARKS
ARMOR-SEALS
ATTACK SPEED-GLYPHS
ATTACK SPEED QUINTESSENCES
For summoner spells take GHOST AND SMITE

Start with a cloth armor and 5 health potion and go to the golem!
After smiting it head to the wolves camp and kill it with wuju style
After head to the wraths and kill the big one first and pop a health potion
After head to lizard and kill it with wuju style stun and smite
Then you should search for a gank if you not go kill the Golem camp and then go back!
And purchase your madreds!


I DONT RECCOMEND JUNGLING AS IRELIA!!!!!