The upper bar of the upper picture refers to the INRI (standing for "Jesus of Nazareth King of the Jews) sign that was placed above Christ's head, and the slanted lower bar was the foothold wrenched loose by pain, yet it also signifies how one of the thieves ascended and other descended to Hell.
I've heard the four equal bars signify the Divinity of God (The vertical line) meeting with Mankind (Horizontal line).
ICXC means Christ in Greek, while NIKA means victory. "Christ Victor", in essence.
The swords, I assume, refer to the strength of Christ and his victory over death, and the circle, referring to the Sun, alludes to Jesus as "The Sun of Righteousness." (Not Son, as I once thought it was a misprint in the Liturgical Book
). However, neither of those things am I 100% sure of.
The double headed eagle was the symbol of the Empire, which was therefore the symbol of the Church. The two heads referred to looking on either side of the Golden Horn where Constantinople sat, that the Empire had dominance in Europe and Asia.