I'm Greek Orthodox and all of my kids have had huge Greek christenings. The most common gift is definitely money. I would avoid Icons or Crosses. The baby needs a cross during the ceremony so they definitely would already have one. Icons are also usually given by the godparent and blessed by the priest. In my family, the baby receives an icon of their Saint plus one of the Blessed Mother.
How much of the ceremony is in Greek will vary according to the church. My church does the ceremony in both English and Greek, but my cousin's church does almost all English.
One thing to know, these are formal ceremonies and all of the orthodox churches I've been too expect people to dress accordingly. This means a suit and tie for men and a nice dress/ pants suit for the woman. My husband is Catholic and at our first christening his family was extemely underdressed. We didn't care, but his family felt a bit uncomfortable.
Also, attending the ceremony is extremely important. There is only one baby baptised at a time, unless you've got twins ;-), and it's a very personal ceremony in which the child is baptized, receives his or her first communion, and is confirmed into the Greek Orthodox church. I know in a lot of other religions it's a quick ceremony with several babies, but for us this is a big deal.
A
DD1 02/04
DD2 01/06
and twin boys 05/09