Sounds kinda odd: "twins were born to them"... Never heard. Is this commonly used?

It's not incorrect, but it's not something you would hear today. It's almost biblical in style.

Can we use preposition "of" instead of "to"?

Hello Julia. You can use the verbal expression born of, but it would sound extremely weird in this context. We tend to use it in the more abstract sense when we talk about concepts: "The United Nations was born of necessity and ideals." However, you sometimes find it in literature when the writer wants to specify the nature of one or both parents: "he was born of a Hungarian father and an Irish mother." "He was born of a prostitute and left in an alley to die."

Thank you, Uly, now it's clear :)

Anytime!