I've loooked around and Oxygene does support this. Partially. It's possible to implement an interface in an expression which will do in many cases:
http://wiki.oxygenelanguage.com/en/Inline_Interfaces

Oxygene does also have anonymous types, but they don't seem to be what I'm looking for:
http://wiki.oxygenelanguage.com/en/Anonymous_Types

To answer you question WILL, anonymous classes are useful when you need to implement an interface or extend a class but you will only need an instance of that class once. An example is the Comparator interface used for sorting. You often only need the comparator in one place and you only need to implement the method 'compare'. In these cases it can be nice to simply use an anonymous class written as an expression when you need it, in stead of going through the trouble of defining a new class and implement it. Anonymous classes also have the extra benifit that they have access to members in the scope they are defined in. Another example where anonymous classes come in handy is when you have to write Swing GUIs.

Of course you shouldn't abuse anonymous classes. Your code can easily become unreadible and imposible to maintain if you use anonymous classes with 50+ lines of code all over the place. They should be used with care; but then they are great feature.