Your FAA certificates don't readily convert into JAA certificates. You will have to sign up for an ATPL theory course before you can take your tests (I think there are 14 tests in all). There is an exception that allows you to directly take the tests, to be eligible you are required to have many flight hours in a multi crew type rated airplane.
Once you have done your ATPL tests, you need to at least take a check ride for instrument flight. The check ride is done in a JAA country. There may be other flights involved in able to satisfy the JAA of your level of qualifications.
As for the on-line schools, you are still required to attend a few weeks of in house training for the test prep.