I thought this would be interesting. Living in Greece allowed me to hear Orthodox hymns in it's ancient Greek form. Before going to Greece, whenever I heard Byzantine Chant, I never really thought about what hymns I was hearing, and they never made sense (as I didn't know Greek at all). Since being in Greece though, I was happy and surprised to learn the various Byzantine versions of the hymns we sing. When we hear these hymns in Greek, it is (interestingly) also the same language many of them were composed in, and I felt that you can definitely tell, as the words and composition easily correspond to one another.
I just wanted to post the Byzantine Hymns along with their corresponding English versions, so that, if you hear the hymns on Ancient Faith Radio, Orthodox Christian Network, or just on a CD, you can identify which one it is!
'Αξιον Εστίν - Axion Estin - It is Truly Meet
Byzantine:
http://youtu.be/u3M-Vf1-mPIEnglish:
http://youtu.be/tpRyYWnzCvQΤρισάγιον - Trisagion - Holy God, Holy Mighty, Holy Immortal
Byzantine:
http://youtu.be/eUMCjDJRyHAEnglish:
http://youtu.be/qPgT7--3Q0EΧερουβικόν - Cherubikon - Cherubic Hymn
Byzantine:
http://youtu.be/fr4mAIibx50English:
http://youtu.be/4d6TbAyUmgoΜεγαλι Δοξολογια - Megali Doxologia - Great Doxology
Byzantine:
http://youtu.be/6SAr8MbYhmAEnglish:
http://youtu.be/BQckHXWer3UΜακαρισμούς - Makarismous - The Beatitudes (Blessings)
Byzantine:
http://youtu.be/VxmRy_ONG28English:
http://youtu.be/yccfPCUNYo0In the Byzantine version of this, you first hear the petition/litany that starts "In peace let us pray...", then "Help us, save us, have mercy on us..." then "Remembering our most holy (Panagia), most pure... and all our lives to Christ our God..." Followed by the prayer before the Little Entrance, then "For unto thee... to the Father, Son and Holy Spirit ... ages of ages, Amen." then the Beatitudes begin.
Σώσον Κύριε - Soson Kyrie - Lord, Save Thy People (AKA Troparion of the Cross)
Byzantine:
http://youtu.be/i8psJVQ1If4English: (can't find one on YouTube, but you know it

)
Αγνή Παρθένε - Agni Parthene - O Pure Virgin (non-liturgical hymn)
Byzantine:
http://youtu.be/Quj_ChDa1ZYEnglish:
http://youtu.be/WkqZbFQb0O0Σήμερον Κρεμάται - Symeron Krematai - Today He is Hung
Byzantine:
http://youtu.be/m2QNbTDjvJ0English:
http://youtu.be/zEkrSh8y50AΤον νυμφώνα σου βλέπω - Ton nymfona sou Vlepo - I Behold Thy Bridal Chamber
Byzantine:
http://youtu.be/any-xnt65FAEnglish:
http://youtu.be/m7PocEBA2s0Ιδού ο Νυμφίος - Idou O Nymphios - Behold the Bridegroom
Byzantine:
http://youtu.be/mbaKjhm__GAEnglish:
http://youtu.be/Trx6nJ6s_eULet God Arise! (Paschal Stichera)
Byzantine:
http://youtu.be/rz3BuDhjYpoEnglish:
http://youtu.be/5avKysnTfjEO Άγγελος εβόα - O Angelos Evoa - The Angel Cried
Byzantine:
http://youtu.be/1LCJo2AiT_kEnglish:
http://youtu.be/_WL-EK5pv0oΧριστός ἀνέστη - Christos Anesti - Christ is Risen
Byzantine:
http://youtu.be/MkrAqsgLAV8English:
http://youtu.be/n8x2CuR8VOkΧριστός Γεννάται - Christos Yennatai - Christ is Born
Byzantine:
http://youtu.be/xU6TcVz_6rgEnglish: (couldn't find a good english video)
I tried to find Only Begotten Son in Greek, but I couldn't. (It was originally written by St. Justinian, yes, the Emperor

)