I want to record how many times or which user accounts passwords were changed using Oracle database auditing techniques. I also want to record any password changes done to system user account.
Auditing can capture when a user changes their own password. If a sys or admin user changes the password of another user that can't be captured in auditing.
You can use this metalink doc (ID 419942.1) to create a system trigger and change it to add an entry in a temp table.