Current international law courts and tribunals have websites, most including free access to (at least some of) their decisions.
They will, of course, be the first place to make breaking/new decisions available.
Indeed, many allow you to watch live video links to court sessions and/or offer an archive of video recordings.
Each website is also a useful starting point to understanding the history of the court, details of its running, staffing and rules of practice and procedure.
The links below list the major electronic resources for holders of an Oxford Single Sign On.
The LawBod shelves, on Floor 3, various series of public international law reports as follows
Internat 100 - General collections
eg International Law Reports Internat 100 I61
Internat 120 - Permanent Court of International Justice
Internat 121 - International Court of Justice: reports
Internat 122 - International Court of Justice: pleadings
Internat 123 - Unofficial collections
eg World Court Reports Internat 123 H886
Internat 130 - Permanent Court of Arbitration
Internat 135 - Collections of arbitral awards
eg WTO Dispute settlement reports Internat 135 W927b
Internat 136 E90a - European Patent Office Reports
Internat 140 - Individual arbitration tribunals: proceedings and awards
Internat 150 - European Court of Human Rights
Oxford Law Citator
The citator is designed to take you from for example, the full report of the judgment in ORIL Oxford Reports in International Law to commentary in OUP's MPEIL : Max Planck Encyclopedias of International Law and/or OSAIL: Oxford Scholarly Authorities in International Law.
When you have read the judgment of the case in ORIL - click on the orange Oxford Citator link in the left hand column. There may be a tree of Related Items on this next screen
For the International Criminal Court see also the free online database below