Do commercial trucks have a right-of-way superior to that of a car when travelling on public roads?

A: No. Commercial trucks must obey the same, and sometimes more extensive traffic laws that an average passenger vehicle does.  All too often, some truck drivers take the "I'm bigger, so you must move out of my way" approach to driving, but you have an equal right to travel on the same roads that they do.  Of course you should always be mindful of your safety when encountering large commercial vehicles like 18-wheelers and tractor-trailers on the road.