How did the Empire find Orta?

We can't be sure, but I assume they must have seen her together with the Wormriders. Iva's story shows the Empire was present in that area . Then it was simply a matter of finding their village.

Why does the Empire want Orta?

What Evren says just before you fight the dragonmares could be an important hint at their true intentions.

"I'm going to enjoy tearing your body limb from limb!" ... and shortly after that: "Get the Dragon first! We can retrieve the girl later". I think this may hint at the fact that the Empire didn't just need Orta to operate the Cradle. It seems to me they needed her for research, making their intentions with Orta very similar to those of Abadd. The fact that in several of the mini-games Orta is referred to as "research materials" in the briefings of the Empire's military reinforces this theory.

Think about this: the Empire had no doubt found similar ruins like the Cradle, but they had only one functional Drone. Unfortunately, because of their complexity (Drones were one of the Ancients' most complex bio-engineered creatures), the Empire is unable to create Drones themselves. The secret of how they were created is only known by the Ancients.

However, the Empire obviously has much more knowledge about humans. So what if they heard about a drone that's half human? Orta could be the missing link they need to create their own drones, which would enable them to control multiple ruins at once, creating dragonmares by the hundreds. And that's not all. Humans are barely capable of handling dragonmares, and have to be protected by a heavy armor, which restricts their movement and makes controlling the creatures even more difficult. Drones, however, were designed to control such creatures, so it would only make sense that the Empire would want to have their own Drones to ride the dragonmares into battle.