What exclusive traits Java has that other languages/platforms don't, that makes it so popular for SOAs?
There's nothing much in Java itself that makes it especially suitable for SOAs. Sure, it offers garbage collection and dynamic code loading and the like, and they're all useful, but they're hardly unique features of Java.
What did make a difference though was the Enterprise Bean specification (which evolved into EJB and JEE). That was basically an adaptation of concepts that had been around for quite a long while in the big-iron space (transaction monitors, that sort of thing) to an OO model, together with the addition of statefulness so that certain types of models were a lot easier to express. The interesting thing is that EJB was a multi-vendor effort; yes, Sun promoted it a lot, but there were many commercial vendors that did implementations of it in their products quite early in the spec's lifecycle. That encouraged a lot of adoption; expertise in Java-based transaction monitors had suddenly become a nice transferrable skill.
Once that base had been established, it grew (e.g., with excellent SOAP tooling support, which superseded the use of CORBA in a lot of deployments) and that's really cemented Java in place. The thing that keeps Java as the king of the SOA space for now is the huge ecosystem of third-party libraries that make it easy to work in the area provided you use Java (or one of the other JVM-based languages, like Groovy or Scala). It's entirely possible to have such libraries in other languages, other environments — I'd expect C# and .NET to do fairly well on this metric — but you typically have to write a much larger fraction of the support layer yourself, and some of that is both tricky and boring to do well; leveraging Java makes a lot of sense if it is keeping you able to focus on the application's business logic and not the support framework.
In short, Java's good for SOA for you because it's good for SOA for many other people (and yes, that's self-reinforcing and sounds tautologous); it's the network effects.