It's due to be billed in June from the tax office (not via electricity bills), and is payable in 6 instalments.
There are quite a few websites that allow you to calculate your tax - this one's as good as any http://enfia.gr/calc.aspx
There does seem to be an age multiplier ("Παλαιότητα Κτίσματος") in the calculation section. The law is published here http://www.imerisia.gr/article.asp?catid=27734&subid=2&pubid=113164502
, and the age factor seems to be in table 2 of article 4.
Running our own property through the calculator, it seems to be cheaper than the "emergency" tax on electricity bills, but I'll wait for the bill from the tax office before celebrating too much.