Human Rights in Malta are protected by the Constitution of Malta and by the European Convention on Human Rights which is part of Maltese law.
EU law is also compatible with the principles of human rights.
Maltese law has to be in conformity with human rights law. The same applies for EU law.
Thus if one feels that his human rights are infringed, enforcement is by recourse through the Maltese Courts.
If the matter is protected by the European Convention, one may have recourse to the European Court of Human Rights in Strasbourg only after exhausting all possible local remedies.
If the issue relates to EU law, the local court may or should (depending on the stage of proceedings) refer the issue to the European Court of Justice of the EU in Luxembourg for interpretation.
The Strasbourg and the Luxembourg courts are not related to one another.
The former falls under the Council of Europe (which is unrelated to the EU) while the latter is an EU institution.