My experience is that the difference lies in where the two forms are used. "Strictly forbidden" is used in signs and notices that want to deliver the message more efficaciously (if you are writing a company's guide for employees, this longer, easily recognised form makes it easier to parse and find what they cannot do).
Actual laws won't use it, however, because it has no legal meaning. And settings that wish to look formal won't use it for the same reason and because it'a pleonasm.