So "off airport landing" might be interpreted as a crash by Joe Public.
How many big jets have successfully pulled off an "off airport landing", presumably you'd only try this if all engines had failed? Is there any data out there about survival rates?
Do you professionals actually train for this in the simulator?

Take away, trees, telephone poles and buildings and add relatively flat terrain and you have a chance if you are in controlled flight.

MCR01

Actually the odds of a happy outcome are not as bad as you probably think. Just off the top of my head, the Gimli Glider, TACA 737-300 that landed on the levee outside New Orleans, and Sully on the Hudson (ok, where the Gimli Glider landed was technically an airport, it wasn't an active airport). The Gimili Glider and the 737-300 were even returned to passenger service post event.
That being said, when we do safety analysis work, a non-recoverable all engine power loss is assumed to be catastrophic - happily that's not always the case.

I did a study of this several years back. For large civilian jet transports, controlled forced landings were catastrophic roughly 3/4 of the time. People tend to be aware of most of the 7 success stories, but few of the 20 plus catastrophic events.

Thanks; I am agreeably surprised that the success rate is so high.
So do pilots actually train for this eventuality in the simulator, or are simulators too simple to allow such training?

It's just another landing until you reach the ground. After that the simulators are also fragile if you overload them

You've lost me. How are simulators fragile if you overload them?

I've heard that before, that those full motion platforms could be damaged by being overloaded by the acceleration commanded by the flight simulation.
I always considered that a bit of a urban legend though. Maybe it happened at some time due to a misconfiguration or a bug.
However I would not believe my colleagues controls engineers at the FFS manufacturers would be so negligent to not limit the control outputs to a magnitude safe for men and machine.
As customer I would not accept it for sure. It's neither complicated nor expensive.

In the simulators that I flew, any landing not on a runway results in a crash. And a crash is a sudden stop. It is just not possible to make a rollout or a slide if you will after a landing on terrain. You would have to freeze the sim upon touchdown (on the simulators I know, all CAE).
So a sim has zero survivability during an “off airport landing” (nice eufimism Boeing!), it is indeed more fragile then the aircraft.
Anyway in all the all engine flame out scenarios that we train there is a runway within reach and you should be able to make that if you are a little bit current at descent planning and mental math.. like the Air Transat that landed at the Azores.

I can’t speak for other carriers, but at mine it wasn’t something that was ever a part of a training syllabus. Dual engine failures certainly were, but associated training/checking revolved around following the applicable drill and/or checklist. The dual engine failure drill and checklists directs the pilots to (amongst other things) establish a descent at a speed and to an altitude within the engine relight envelope. The focus is on achieving a successful relight of at least one engine.

The only time I might have been required (in the simulator) to attempt a landing after a total loss of engine thrust might have come as a part of my carrier’s captain upgrade process which included two simulator sessions during which a candidate could expect to be given situations like this to handle. Needless to say, I spent some time practicing dead-stick landings (amongst other things) from 10,000’ to the runway. However these two simulator sessions were strictly an internal requirement for captain upgrades and not a regulatory requirement, hence normal recurrent training and checking protocols never required this kind of event.