As far as I can tell, JAXP by default supports W3C XML Schema and RelaxNG from Java 6.
I can see a few APIs, mostly experimental or incomplete, on the schematron.com links page.
Is there an approach on validating schematron in Java that's complete, efficient and can be used with the JAXP API?
Jing supports pre-ISO Schematron validation (note that Jing's implementation is based also on XSLT).
There are also XSLT implementations that can be very easily invoked from Java. You need to decide what version of Schematron you are interested in and then get the corresponding stylesheet - all of them should be available from schematron.com. The process is very simple simple, involving basically 2 steps:
JAXP is just an API and it does not require support for Relax NG from an implementation. You need to check the specific implementation that you use to see if that supports Relax NG or not.