There are currently two institutions that hear European Union cases: the Court of Justice (also informally known as: the European Court of Justice (ECJ)) and the General Court. The General Court was originally called The Court of First Instance (CFI). Between 2004 and 2016, there was also another specialised court called the Civil Service Tribunal (CST) to deal with cases relating to the staff of EU institutions. The General Court now deals with case involving staff of EU institutions.
(or its official title Court of Justice of the European Communities) was created by the Treaty of Rome, and interprets an applies European Union law as found in the treaties and legislation.
was created in 1989 to assist with the case load of the ECJ, and principally hears cases dealing with competition law, dumping, subsidies and staff grievances. Decisions of the Court of First Instance can be referred to the European Court of Justice for appeal.
Each case is given a case number when it is referred to the Court. Cases before the European Court of Justice have the prefix 'C' and cases before the General Court have the prefix 'T' e.g. T-168/96: Action brought on 22 October 1996 by Catherine Patronis against the Council of the European Union.
A full citation to a case in OSCOLA would include this number plus the reference to where you can find the text of the case report
A typical OSCOLA citation to an ECJ case looks like this:
Case C-132/92 Birds Eye Walls Ltd v Friedel M Roberts  ECR I-5579
This is interpreted as European Court of Justice (C), year it was added to the register (92), case number (132), party names (Birds Eye Walls Ltd v Friedel M Roberts), year the report of the decision was published (1993), abbreviated title of the series of reports the case was published in (ECR), volume (I), and the first page (5579).
European Union cases are officially reported in two publications:
The 'C' series publishes court orders and judgements, plus a list of cases filed before the ECJ.
(usually referred to as the European Court Reports ECR) - this is the official reporter for EU court cases, the publication is divided two main sections, Section I which contains European Court of Justice cases and Section II which publishes General Court/ Court of First Instances cases.
Another source that you should be aware of is the commercially published Common Market Law Reports (CMLR) (not to be confused with the Common Market Law Review (CMLRev) which contains journal articles).
The CMLR is published weekly, each volumes four months and has its own index. All England Law Reports is another unofficial report that publishes selected EU cases.