How to test a DTS package created for data insert update and delete? What should be considered in the above case while testing it?What conditions are to be checked if the data is inserted, updated or deleted using a text files?

Data Integrity checks should be performed. IF the database schema is 3rd normal form, then that should be maintained.
Check to see if any of the constraints have thrown an error. The most important command will have to be the DELETE command. That is where things can go really wrong.
Most of all, maintain a backup of the previous database.