In aviation, flights are diverted to a different airfield, but flights deviate from their flight original plan. So there is an element of active/passive. Air controllers or pilots divert a flight usually for some kind of safety reason. Anytime an aircraft breaks from the flight plan the pilot filed, it deviates from the plan. If the aircraft was supposed to fly Route A, but took route B, it deviated. So a flight is diverted (passive), but deviates (active).

You are correct that you can "divert a flight" but not "deviate a flight." The two words have different meanings. "Diverted" is correct here. "Diverted" means "an intentional, major change" such as going to a destination different from what was planned. If they expected to land in Gatwick and instead they landed in Luton, they were "diverted." "Deviated" refers to a path or a route. It means that something took a different direction, perhaps only a slightly different direction, than planned. It also suggests a mistake rather than a planned change. "When the captain took the noon sight, he found that the ship had deviated quite a bit from its course, and he ordered the helmsman to steer two points north to correct it." "If you use a magnetic compass, you must correct for the deviation from true north."

Nothing related to prepositions, just sounds better when talking about directions or travel. However, if you were examining it from a statistical point of view, deviate would be better because you are comparing planned with actual results.