Can Ospreys land without running engines?
Welcome to AviationStackExchange and to provide a short answer to your question, yes there are autorotation measures that are similar to those featured on helicopters. The basis for most of my answers pertain the unique drive shaft system, which allows for redundancy between proprotors, something other twin-engine fixed wing aircraft usually lack, so here's a diagram for some reference: 



As for the detailed answer, I'll split it into three parts: One engine failure, total engine failure, and a stuck rotation mechanism.


The two RR T406 type engines of the V-22 are connected by a driveshaft, which means that if one engine loses power, the other, provided that it is in good working order can deliver power to both proprotors through said shaft. It lacks the power to actually hover on that one engine though, so it has to be glided down, and protocol presumably dictates a powered glide to somewhere safe.
When both engines fail, autorotation just as on a helicopter is instructed, however, due to the fact that the proprotors are about a third of the diameter of conventional rotors means its low rotational inertia results no autorotation will significantly reduce the impact from a total failure. In other words, it can't really glide like a plane and won't autorotate like a helicopter. It's getting the best and worst of both worlds.
As long as the engines are working, the V-22 can land and take off in both configurations. However, there's an approximately 18-20% (Wikipedia quotes 18, Boeing claims 20) increase in flight efficiency in the turboprop aircraft configuration over the VTOL setting. I can only imagine that number goes higher by 10-15% during takeoff and landing. Planes are simply more efficient this way.


So, yeah.