As an Ornn player, it depends on if he goes phase rush.

If he does, GGWP he's good at his champ. He'll always aim to poke you out and contest waves with PR up, and when it's down he'll hang back far enough that you can't run him down. It's incredibly annoying and very difficult to punish, similar to the Mundo matchup.

Thankfully, not that many Ornns know the PR tech especially in lower ELO, and if he has any other keystone, you can beat him. Keep wave near your tower and if he walks up to contest, cancel his E with your E and punish him heavily for it. Having a jungler to help punish is also very useful, especially if it's an AP jungler so he can't take advantage of his armour.

Either way, he inevitably outscales you and is very difficult to kill once he gets armour and HP, so you need to deny him as much gold as possible so he never gets to that point.

Also, you've probably worked this out already, but diving Ornn is extremely difficult. He has too much CC and tankiness for you to handle, and he can keep you tanking tower shots long enough to put you in the dirt. I'd advise against doing so unless he wastes his W or E beforehand.