St Paul is pictured with a sword because that was the instrument of his martyrdom. Other saints may be so pictured for similar reasons, or because they were military saints, such as St Michael, St Martin, St George, St Joan of Arc, etc.
It is also considered the Sword of Justice for one who is the defender, St.Michael is often depicted in armour with a sword.
St. Nicholas of Mozhiask is depicted holding a church or city in one hand and sword in the other. He was defending the city against a plague or is defending the Church.
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