You can kite, but you won't deal as much damage as his W just did to you to cuz shield. And if he really wanted to, he'd just Q (cuz huge range) -> E. Ofc Quinn is the only one who can say no to the E part, but she still lost the trade due to the old broken W damage and shield.
You can't counterpoke, cuz W shield and if your poke range is equal to or less than his W range you're gonna eat the W.
Of the list of immobile melees you stated (I'm a top lane main btw):
Illaoi - No. Atleast not until 6 but he has no reason to all-in Illaoi, saving his E to escape a potential ult setup. Pulling his soul does nothing since he can easily get his soul back in seconds via the multi-tick damage of W, a Q and 2 hits of E -> AA to effectively reduce the duration to only 1 second (and no Illaoi can't dodge a reaction QE due to the cast time on soul pull). Top this off with the fact that his W range was able to match Illaoi's Q and there's just no way for Illaoi to kill him in this braindead matchup.
Darius - Maybe. Ornn's QW poke was enough to get Darius wittled down to a point where Ornn doesn't have to be scared of him. Darius' attempts to counterpoke are met with a Brittle proc and a fleeing Ornn. Pulling the Ornn results in Ornn using his E to escape. Rinse and repeat. However, one misstep on Ornn's part could easily seal his fate. (Note that this is before Conqueror existed, giving Ornn the upper hand in the rune department via Grasp)
Vlad - Maybe. Ornn just runs out of mana. That's the only issue here. If it weren't for that Ornn would win via simply QW -> walk up and auto attack. Vlad using pool to avoid the auto or W is equivalent to just taking the attack anyway due to the 20% health cost. Ofcourse you aren't gonna kill him as Vlad, but you can force him to recall now and then.
Urgot - Hah no, never. Urgot got demolished by Ornn on release. Don't need much explaining here, Ornn simply could just outtrade him and poking wasn't viable since it was met with the good ol QW -> walk up AA. And at no point in the game could Urgot outdo Ornn in a 1v1. I was an Urgot main at the time and this matchup was simply disgusting.
Tahm - I really have no clue. I never touch this thing. Don't know his damage numbers but with the regen passive and %health damage alongside his sticking potential I could see it working.
Yorick - Pre-6 no, post-6 yes. Yorick main btw. It's an absolutely tricky matchup cuz none of your poke damage sticks but your all-ins do. Only problem is his all-in trades beat out Yorick's. So to even out-trade him at all you had to EW with 4 ghouls, Q'ing is never an option because his W + Brittle AA + Grasp and the fact that he can E the wall for a point blank knockup. Typically killing him or even shoving him out of lane this way was impossible, the minor damage from each trade was simply to wear him down for a hopeful jungle gank. You can't lock him in the wall for endless ghoul beatdowns either, cuz his E breaks it. Post-6 Yorick has the upper hand with Maiden making him excel in drawn out fights (aka vs tanks), but pre-6 hell no and when Maiden isn't up post-6 hell no.
Anyway, there's a reason Ornn was banned almost every game until the nerfs.
Note that all of these are in regards to killing Ornn in lane. Winning lane is a whole separate matter. The key to winning vs old Ornn wasn't to kill him but rather to win in other aspects such as scaling and whatnot. The point was to simply "survive" the lane. The problem with this as well is that Ornn "scaled" way better than almost every top laner. His ult's utility in teamfights was simply unmatched especially alongside how tanky he was and how huge a damage threat he was in teamfights.
Now with new Ornn, trading with him is possible due to W having longer gaps between uses and Brittle not lasting until W is back up like it used to. It solved pretty much every champion's counterplay issues with him, especially the immobile melees.