Hi Manish,
I would not be able to say much on Courts of Inquiry. Both are constituted under the Industrial Disputes Act. Courts of Inquiry are constituted for a specific dispute, but their constitution is very rare (I am yet to come across one).
Industrial Tribunals, along with Labour Courts, function in every state just like any other court (District, High Court, etc.) to resolve industrial disputes.
Any industrial dispute is first taken up by the Conciliation Officer. Once it fails at conciliation, the Conciliation Officer sends a failure report to the Government, on which the Government decides whether to refer the case for adjudication or not. If the Government decides to send the case for adjudication, it is referred to either a Labour Court or an Industrial Tribunal. In the Industrial Disputes Act, it is specified as to what type of cases should be referred to Labour Court and what type to Industrial Tribunal (This is the only difference between the two). The decision of the Industrial Tribunal/Labour Court can be challenged only in the High Court.
The second point is that employees or employers cannot directly go to the IT/LC (Industrial Tribunal/Labour Court) except in some cases where direct monetary loss can be proved.
The third important point is that IT/LC are framed to adjudicate on industrial disputes and therefore other courts like Munsif or District Courts can take up industrial disputes.
KKT