After having checked a number of parishes, it seems that some do the unction service and some don't.... I wonder why that is.....
Fr. Calivas has this to say about the history of Holy Unction in Holy Week:
It is not altogether clear how and when the Sacrament of Holy Unction came to be celebrated on Great Wednesday. It may be related to the fact that in Christian antiquity penitents were received and reconciled during the course of Great Week. The sacrament of Holy Unction may have been part of the reception process for lapsed Christians, who were reconciled to the Church through the sacrament of Penance.
It has become the practice among the Greek Orthodox in the United States to conduct the sacrament on Great Wednesday evening in the place of the usual service of the Triodion. Pastoral considerations have dictated this custom.
On a grand intuitive level, the idea that the service is a vestigial "liturgical echo" of the reception of the lapsed makes sense. Penitential anointing was a common means of reception into the Church well into the later years of the Eastern Empire. But I imagine its popularity through the Tourkokratia to the present day may be more practical.
This is a Sacrament for which there are few, if any, traditions that restrict participation. I have yet to meet an Orthodox Christian of any stripe who believes one must fast for three days and go to confession and do 3000 prostrations before being anointed with Holy Oil. But I have met plenty who believe one must do just that before receiving Holy Communion. (Or who simply believe they are too unworthy to receive more than a couple times a year.) Thus, Unction offers an accessible means for EVERYONE (even the "unworthy") to receive a sacrament. That's quite an attractive alternative, especially in a period of time where there are so many Eucharistic services going on.
Of course, that's just a conjectural explanation for why it has become such a popular unwritten tradition. Strictly speaking, it is not part of the actual Holy Week services called for in the Typikon. It can be celebrated whenever one feels the need, and, obviously, people feel the need during Holy Week.