Cessna 182 pilot reported engine failure during climb on a skydiving flight. After skydivers jumped from aircraft; the pilot performed a dead-stick approach and landing at nearby airport.

Narrative

While climbing through 9;700 MSL (4;500' ASL) with one pilot (myself) and four skydivers on board; the engine catastrophically failed; accompanied by a loud noise and vibration and followed by oil covering the windscreen; and then what appeared to be smoke filling the cabin. I immediately closed the throttle; set mixture to idle cutoff; moved the fuel selector to the closed position and shut off the main power bus and all lighting and electrical controls. I told the skydivers we had an engine failure and what appeared to me to be an in-flight fire (it was actually oil that had vaporized when it struck the exhaust manifold). I asked the skydivers if they were prepared to exit. They replied affirmatively; so I invited them to do so. They opened the door (clearing the oil vapor from the cabin) and rapidly departed the aircraft. All subsequently landed safely.I then performed a slip and steep left rolling maneuver to close the door; continued the turn and began a downwind glide toward the airport; four miles distant. When within one mile of the airport; I turned on the radio and [requested priority handling] to ZZZ Approach; stating that I had an engine failure and possible in-flight fire; and that I was going to attempt to land on runway XX at ZZZ [airport]. Approach responded that there was no traffic in the vicinity and that they were available for anything I needed. I set the transponder code; added 20 deg manual flaps; then made an abrupt; low and short downwind-base-final turn to a smooth dead-stick landing into the wind on runway XX. I made a radio call that I was on the ground safely; which was relayed by another aircraft to ZZZ Approach.No fire had actually occurred.