Martin and Paul are right: It sounds like you have a problem when you are creating the data as
you should not be able to create orphan records like this. If your DBA doesn't know how to maintain data integrity (which is one of the fundamental principles of the relational data model), then your company needs a new DBA. You (or your DBA) need to stop creating bad data, so make sure your FK constraints are properly defined and enabled where appropriate, and that you are trapping any errors during data load/migration etc.
Fix the bug, don't build a half-baked tool to maintain the results of the bug.
You can use SQL and your database's data dictionary to work out the relationships between tables where FK constraints have been defined, but of course this won't help you if no FK constraint exists in the first place. You can then use this knowledge to run SQL queries to find the orphan records by querying the relevant key columns on the parent and child tables. In Oracle, for example, you can use the MINUS operator to do a simple set comparison between the keys in each table:
SELECT DISTINCT child.keycol
FROM child
MINUS
SELECT parent.keycol
FROM parent
This will give you the list of keys that exist in the child but not in the parent.
As for visualising the data model,
Oracle's free SQL Developer Data Modeler allows you to generate a schema diagram from the database. SQL Developer is a really useful free tool for Oracle-based development, so if you are developing applications on Oracle you should be using it.