is it possible to use "of" instead of the possessive S when referring to people (or animals)?

The sister of my father. <-- Not used at all? I think I heard it. Just once though...
My father's sister. <-- OK

The sister of the guy on the left.
The guy on the left's sister.

The sister of the guy we met in Santa Barbara.
The guy we met in Santa Barbara's sister.

Thank you Emotion: smile

You can always do that. The problem is that sometimes it sounds awkward and can in fact be difficult to say. In your examples, #1:2 is smoother; in the other two cases the first option is smoother.
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Interesting... Thanks Emotion: smile

You hear it both ways. It depends somewhat on the context. The version with 'of' seems a bit more formal to me.