There are three types of factory test named (1) Routine test (2) acceptance tests and (3) type tests. Normally, these test categories are standardised by varios codes and standards.
In transformer routine tests, I guess there should be dry frequency high voltage test, winding resistance test, insulation resistance/volume resistivity test, temperature rise test, Partial discharge test etc.
Accepatance tests are categories of test designed to witness by customer as agreed by manufacturers at the time of order placement to accept the lot of transformers ready for shipment.
Type tests are categories of test includes some distructive test too. At the end of type tests, the equipment is out of life and can not be used. Normally, these tests are conducted on one transformer selected randomly from a big lot of transformers.
Which country are you in? Please find out national standards of your country. Otherwise look brochure of IEC, IEEE, BS, IS, VDE etc to research applicable standards.
Where you came across, the requirement for 'Overall test' of a power transformer? Standards call for 'routine','type' and 'acceptance' tests. Please provide more information on,what is expected of such 'overall' test.