What specific tests need to be performed under Database migration from DB2 to Oracle?
Normally for a straight forward data migration it is enough to know that all data is complete, valid and accessible for the application. Typically subtle differences may pop-up with some data-types like those with date, time, binary fields and long text fields.

In a straight forward data migration, data from table a field a goes to the new system in the same table, the same field. A good check to validate this could be done by computing a MD5 check-sum on all fields of all tables, both in source and target tables. Any difference here shows there is a problem in the migration procedure or software. Make sure to have the same formats in place for the MD5 computation; for example, make sure that the date formats are the same on both sides.

The application has to be tested, that's for sure. What the strategy should be is hard to tell, every application has it's own challenges. If all logic is known and standardized, it could work by making a simple test application that accesses all different field types and see how the interaction goes. In the end a regression test will be needed.