The EU issues Regulations, which have immediate effect in member states, and Directives, which member states are required to implement in national law, so it's not too far wrong to talk about EU law. http://en.wikipedia.org/wiki/European_Union_law
Yeah, I know. You should also mention the European Court of Human Rights, whose decisions override national courts (of course, the decision is usually "this case not is our job, go with whatever the national court told you".)
Caveat: IANAL (but my wife is).