My guess is that this was a delayed commemoration of Greek Independence Day, March 25th, 1821, when Bishop Germanos (Herman) of Old Patras, raised the flag of Greece, upon the conclusion of the Divine Liturgy for the Annunciation Feast Day, announcing the rebellion against the barbarous Moslem Turks, who had occupied Greece, the other Balkan States, and the Northern Mideast, since the mid-15th century (+/-). It seems like the faithful were also reminded that the Turks also are currently (since July, 1974) illegally occupying one third of Cyprus (Kypros); the matter of the occupying Turks' charging admission to a confiscated monastery has been in the news recently. The flag you noticed is the Naval Flag of Greece. The table with the flowers and the picture, was probably for a Memorial (Mnymosino) Service, the picture was of whoever was being memorialized; koliva (primarily boiled wheat) was probably on the table, too, if there was no koliva, it may have just been a Trisagion Service (not including "Blessed at Thou O Lord, teach me Thy statutes..."). Today is the anniversary of the birth of Theodore Kolokotronis, a noted general in the Greek army during the revolution, so, perhaps the Memorial Service was for him, perhaps that was the reason for the events you witnessed. Are you in the province of Arcadia? My recollection is that Kolokotroni was an Arcadian. Commemorating the dual holiday's of the Feast of the Annunciation to the Theotokos and Greek Independence Day is not uncommon in Greek Orthodox Churches, though such commemorations within the church, are very much in decline in America; what you witnessed exceeds anything I've ever seen in America. Typically, at the most in the U.S., there's only a short Greek School play. (My parish priest had to tell the Greek School they were not to play Greek patriotic music in church). I don't have first hand knowledge about how common what you witnessed is in Greece or Cyprus. In the past, laity have been given a blessing to speak of such maters in the churches. During WWII, Archbishop Athenagoras of America, (a friend of President Roosevelt's) of blessed memory, (later Ecumenical Patriarch) had authorized informed laity to speak in the church, following the sermon, about the patriotism associated with America's fight against the Axis Powers. (The Metropolitan of the Holy Metropolis in which I live, prohibits laity from speaking in church--I imagine exceptions can be made, with his permission.)
The dual celebrations of March 25th are largely responsible for the Greek government's pressure upon the Archbishop of Athens to convert to the civil, New Calendar (in 1923?), so that both holiday's would be commemorated on the same day.