Irelia's Skill Max Order: Q → E → W
Level 1: Irelia starts Q or E, usually E. If she starts Q level 1 be careful because she can get her stacks on the first 3 minions to do a good trade. You can Quinn Cheese level 1, and then zone her off the wave so she can't use her Q, and is forced to sit there to use E to last hit. Zone her off as much EXP as you can. Slow push first wave and the ideal position is to zone her so you're in between the wave and her. This forces Irelia to be out of XP range to delay her level 2 spike.
Level 2: You will be level 2 slow pushing the wave. Still zone her becasue she will be level 1, and when the cannon wave comes, push the wave as fast as you can with autos. If you play this correctly, you will be level 3 and Irelia will be level 1. You can either dive her when the cannon wave crashes (especially if jungler comes, ping a dive if she's level 1 and your JG is near) or you can cheater recall, which is backing and buying an item as the wave bounces back to you. When she gets level 2, be careful because she can instantly stack her passive and aim for a big trade against you.
Level 3-5: You must manage the wave properly from here onwards. Do not let irelia freeze the wave in front of her tower because this allows her to instantly get her 5 stacks with ease. The best way to play these levels is for you to freeze the wave in front of your tower if possible. This makes it hard for Irelia to stack her passive, which is her win condition. If she lands E on you, Q-E-AA in one quick combo, which will proc phase rush and allow you to escape since she's blinded. She can't Q you a second time if blinded.
Level 6: If Irelia has wave frozen and is level 6, you must be careful because she can 1 shot you with her passive fully stacked. You cannot let irelia freeze post 6 especially, so call for jungle help if she has a freeze. If Irelia lands R on you, save blind for her Q. When she Qs you, her dash brings her behind you. You will throw your Q behind you when she dashes, and then instantly E-AA after you land your blind. This combo will proc Phase Rush, grant you W speed, and Irelia is blinded. PR gives you 75% Slow Resistance, which renders her 90% slow on her R to be useless. You can even run through her R since it doesn't slow you, and since she's blinded, she can't get her Q resets on you. When her nearsight wears off, you will be too far for her to Q you again. See this clip for an example.
Play level 1 to let her push, and freeze in front of tower. Don't push against irelia. Freezing early is good because she can't spam her Q and bully you. She wants to freeze, but if you freeze, she can't bully you. Be aggressive early, and save vault to dodge irelia E OR vault away from irelia if she lands E on you.
Even if she stuns you with E and gets a Q reset, if her E stuns you and she Qs on you, vault away with auto-e-auto, and then if she dashes again, your phase rush + w max allows you to out run her with ease after.
Her E range is 775, but it's easy to tell when she wants to use it because she'll put the first mark of her E down before she engages.
It's quite easy to dodge with W max! Her Q range is 600, which is 75 more than our auto range, so keep that in mind! Also, our E does not reset her Q if we are marked, BUT if you vault irelia before she Qs a minion, Her Q will go on cooldown lol.
Do not try this at home though because her Q is so so fast, and this requires smurf-like prediction timing.
IMPORTANT: If you blind irelia, she CANNOT Q you if you are outside of nearsight.
Use this to your advantage in laning phase, and also when she tries to all-in you post 6.
NOW, irelia is level 6 and you're scared.
When irelia dashes onto you, her character goes slightly behind you, so it's hard to land Q on her after she dashes towards you.
The best thing to do is to predict her engage.
Irelia wants to dash on a minion likely before ulting you, so anticipate this.
When she ults you, she will follow with Q 99% of the time, so retaliate with your Q when she ults.
Now, irelia will Q onto you, and you then vault instantly.
Irelia is blinded, so now you can outrun her, and by the time her nearsight wears off, she is now too far to Q onto you again.
Master this, and Irelia should never be able to full- combo you with her ultimate. :)