In Java, are enum types inside a class static?

Yes, nested enums are implicitly static.

From the language specification section 8.9:

Nested enum types are implicitly static. It is permissable to explicitly declare a nested enum type to be static.

It wouldn't make sense to make an instance-level (non-static) inner enum class - if the enum instances were themselves tied to the outer class they'd break the enum guarantee -

e.g. if you had

public class Foo {
   private enum Bar {
        A, B, C;
   } 
}

For the enum values to properly act as constants, (psuedocode, ignoring access restrictions)

Bar b1 = new Foo().A
Bar b2 = new Foo().A

b1 and b2 would have to be the same objects.