Do all the following word orders sound natural? Is there a difference in meaning?

It is a matter of emphasis. Without context, the most natural option is

• El hombre leía el libro a la niña

But you might want to emphasize "la niña", in which case you can mention her first. For example:

• El niño leía el libro solo porque ya había aprendido a leer. A la niña le leía el hombre el libro.

Or you might want to emphasize "el libro" and mention it first:

• Había una revista y un libro para entretenerse. La revista la leía normalmente el niño. El libro se lo leía el hombre a la niña.

The additional se is a case of a duplicate indirect object pronoun, similar to le in sentence 3.

The other example (sentence 2.) is less common in spoken language, and sounds more poetic/literary to me. But it is also correct: you might well find it in a novel or a poem.