does vex stun ori units when they are turned to units

No — Vex, Apathetic only triggers when an opponent plays a unit, and Orianna's Lady of Clockwork ability ("choose a friendly gear — it becomes a unit gear with Might equal to its Energy cost") doesn't play anything: the gear is already on the board and just gains unit properties, so no "play a unit" event occurs.

This is the same distinction the FAQ draws for tokens: tokens that are played trigger Vex (FAQ #9833), while tokens merely created or put onto the board don't (FAQ #10054). A gear changing card type in place is even further from a play — nothing enters a zone, so Vex never sees a trigger, and neither the Stun nor the "can't move it this turn" clause ever applies.

If Orianna's controller instead plays a real unit (or a token unit via a play instruction) while Vex is at a battlefield, Vex triggers on that as normal.