Is Opera 40 incompatible with Java?
Chrome is incompatible with Java now because of loss of NPAPI support. Is Opera 40 also incompatible with Java?
Yes. Opera is based on the same renderer as Chrome. They dropped support for NPAPI some time ago.
That said, Oracle, the makers of Java, have also announced they will drop support for NPAPI. You've got 3 to 9 months, depending on the release date of Java 9, before its gone.