To use cascading deletes, you would need to have foreign key constraints between the tables. You would set up the cascading delete rule when defining the foreign key, like so:
ALTER TABLE contactdetails ADD
CONSTRAINT FK_contactdetails_company_id FOREIGN KEY (company_id)
REFERENCES organizations (idOrg)
ON DELETE CASCADE
This would tell the db that when a row is deleted from the organizations table, if there are any rows in contactdetails that reference it, those should be deleted as well.
As for whether this is a good idea or not - that's a matter of opinion. Personally, I don't like to use them since it makes it too easy to accidentally delete lots of data that maybe you didn't intend to delete. But others will disagree I'm sure.