One of the thematic and practical aspects of telekinesis is moving things at range. But in practice, only Irelia's ult moves her blades at range. Although one could explain her Q as her holding on to her flying blade.
In any case, I really think her abilities should be more of the ranged variety with her AAs being focused on close-ranged combat. She should be able to throw her blades to pierce an enemy for damage at range, make stationary walls and shields, or throw them around to do a lot of damage in small AoEs. I also don't like how her scaling is all over the place. And her passive, while useful, simply does not match her flavor. Neither does Hiten-style. But we can fix that.
This begs the question what about her auto-attacks? Should they be close range melee, or long range poke? If we go lr poke, we risk turning her into an ADC, and an exceptionally powerful one at that. So I'm thinking keep her AAs melee range.
I like the suggestion below of changing Irelia's ult to a switch like Elise's ult or Jinx's Q. Swap between Hi- and ten sub-styles. Whichever mode is active can determine what kind of on-hit effects she gets on her other abilities, or even completely different abilities. Personlly I would make abilities on the same skill share a similar theme.
Passive: While in Hi-style Irelia gains 5% Lifesteal (too much?). While in Ten-style Irelia's attacks gain bonus magic damage based on scaling AP. (True Damage would be OP for an always on passive ability.)
Q: PIercing Blades.
Hi-style: For every level in Piercing Blade, Irelia can summon 1 spirit blade. Irelia fires all her blades at once in a line towards the cursor. On contact with an enemy unit the enemy struck will be rooted for .25 sec per blade and will take a small amount of magic damage per blade based on scaling %AP. Essentially, this is just like Morgana's Q. But Irelia is pinning her enemy to the ground with her swords for a short duration.
Ten-style: For every level in Piercing Blade, Irelia can summon 1 spirit blade. She can fire each spirit blade in a line towards the cursor, dealing physical damage to enemies it passes through. Applies on-hit effects. Deals magic damage based on %AP+ some flat damage. Similar to Transcendant Blade but not as powerful.
W: Flying Blades.
Hi-style: Irelia dashes to an ally, reducing all physical damage dealt to them and herself by 50% for the next 1/2/3/4/5 seconds.
Ten-style: Irelia dashes forward to strike her target, dealing physical damage and applying on-hit effects.
Both: If Irelia gets a kill, the cooldown on this skill is reset and refunds 35 mana.
E: Spinning Blades.
Hi-style: Irelia spins her blades vertically in front of herself forming a shield of blades that protects Irelia from projectiles. Any enemy caught in the blades is stunned for the duration of the ability and takes physical damage for the duration of the ability based on scaling AD+some flat damage. Duration: .5sec per level.
Ten-style: Irelia spins her blades horizontally around her, dealing physical damage in an AoE (2x AA range?) based on scaling AD+flat damage. Enemies caught in the effect are slowed (20/30/40/50/60%) per level for .5sec per level.
R: Hiten Style.
Swap modes. Very short cooldown, if any. No cost. Available at level 1.
So what does all this mean? Swapping modes does not reset your skills. You are not Elise. You cannot Q in, pop an ult, and then ward hop out. You are not Lee Sin or Zed. Both your dashes are on the same skill. The potential for flashy LCSBigPlays is definitely there. She can root, swap, dash, slow+damage, then dash out if she gets a kill with her combo. But she doesn't get the dash reset without a kill. So you had better be sure of yourself when you go all in.
Note: I'm thinking having her dash reset on monster and minion kills might be pretty nifty. Or OP. Not sure which yet. Probably OP.
She has sustain or extra damage based on mode. Not both. She no longer does true damage. I know folks will miss that. But on an always on passive, that would be either extremely OP or nerfed to uselessness. She is definitely a melee. But she has some poke. So she should still be viable top lane. Her sustain and damage can make her viable in the jungle. Rush Q levels and poke like a boss. Rush E levels and be a wave-clearing goddess. Or rush W levels and... well, be average.