Title 40: 200: Search of employee vehicles:
Employers of this state that conduct employee-owned vehicle searches of its employees shall conduct such search on the property of the employer only. Searches that are conducted on property not owned or rented by the employer shall require a search warrant issued according to law.
So, in Oklahoma, employers can search your vehicle if they have a valid reason to do so. I would assume if they have the right to do this, then they can search your backpack, purse, tool chest, etc, as long as its on property owned by the employer.
Just to be clear, that text doesn’t grant an employer a “right” to search your vehicle or grant them some sort of authority. They can have a policy that’s a condition of employment, and you can refuse it at risk of being terminated. What the text is telling them is that they have no right to do it off of their property.