What are my rights as an employee at a private owned business in Virginia. If I never signed any agreement am I forced to take a drug test.

As a general matter, your employer may condition your employment on your satisfactorily passing a drug test administered from time to time, even if you have not signed anything. If you refuse to take the test, you may be sacked. Overtime hours are required to be paid in accordance with federal law, and you have a legal basis for recovery if they are not paid.