Why do images of saints often depict them with unusual hand gestures? Many saints are often depicted holding a book or some other object. However, I have noticed that there are quite a few that have unusual hand gestures. Why is this?
Augustine of Hippo
Index finger, middle finger, and ring finger together, other fingers spread out

Ignatius of Antioch
Ring finger and pinky against thumb

Justin Martyr
Index finger against thumb, middle finger extended
I'm going to assume that the modern vulgar meaning for this gesture was not intended.

Cyril of Jerusalem
Index and middle fingers crossed, ring finger against thumb

John Chrysostom
Ring finger against thumb, back perspective
Wordpress:
Ancient Greek and Roman orators used an established series of hand gestures when speaking.  Since some of the oldest Orthodox statuary originated in Rome, it is likely their hand gestures were adapted from those of the Greek and Roman works when depicting religious figures to emphasize the message the painter or sculptor wished to convey.  Since orators of the time often raised their hand when speaking to assert authority, paintings and statues of Jesus and the saints might have adapted this to convey authority and a  blessing.  We see this today when the Pope blesses a crowd of the faithful.

Gesture of the Orator:
Illustrations of various hand gestures from antiquity with explanation of their meaning.

Roman &amp; Greek sculptures:  Photos showing hand gestures.