Here is the statute about carrying in a Secured container:
§ 18.2-308. Personal protection; carrying concealed weapons; when lawful to carry.
10. Any person who may lawfully possess a firearm and is carrying a handgun while in a personal, private motor vehicle or vessel and such handgun is secured in a container or compartment in the vehicle or vessel.
That pretty well eliminates a Commercial Vehicle.
I have no idea about Open carry though. I've always heard truckers complain that they can't have a weapon of any kind...but I don't know where that comes from.