The basic sentence is: "It is broadcast around the world and nobody need ever be without it." The phrase "who has access to a radio with short wave" is an adjective clause that modifies "nobody". An adjective clause is a clause starting usually with "that", "who", "whom", "whose", "whoever", "whomever", or "which", and which modifies a noun or a pronoun just as an single-word adjective would.

If it's any consolation, I'm a native English speaker and I have a hard time understanding the sentence structure of that sentence. Some of it is flat out incorrect, like "It is broadcast" should be "It is broadcasted." The closest explanation I could give for the second part is that the middle part, "who has access to a radio with short wave" is a clause that is describing the noun "nobody." (I would almost think of the entire clause as one long adjective). It might help to take out that clause to understand the second half, which would make it "nobody need ever be without it." In this case, "it" is the broadcast. In French, it would be similar to "personne qui (clause) n'a besoin de s'en passer" Does that help?

Don’t feel bad about not being able to understand that sentence. I don’t understand that sentence. 🌈

We normally say short wave radio. Some radio frequencies are short wave....they tend to travel farther. The English isn't great. It should be more along the lines of: anyone who has a short wave radio should always be able to access it.