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:
- apply the skeleton XSLT on your Schematron schema to get a new XSLT stylesheet that represents your Schematron schema in XSLT
- apply the obtained XSLT on your instance document or documents to validate them
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.