The only thing I've noticed lacking from an Orthodox wedding ceremony that is in a "traditional" American ceremony is the ability to write your own vows/exchange vows and the use of non-church music (although some has been adopted for church purposes).
There is still a kiss at the end of the service, there is an exchange of rings, there is the bride walking up to the solea to meet her husband, there's still bridesmaids and groomsmen, there are flower girls and there can be a ring bearer, there can be a best man and woman (although sponsors do most of the actual in service things), there is also to boot the possibility of a live choir singing which made my wedding all that much better.
You don't get "Here comes the bride", "Fur Elise", or "Ave Maria" but there is an Orthodox version of Ode to Joy by Beethoven, and there are songs that I think are more beautiful than those previously mentioned within the Orthodox liturgical music (Rejoice O Virgin Theotokos, Rejoice O Isaiah, etc.)
Flower girls/ring bearers may not be permitted, depending on the priest. I happen to know a local priest who threw an absolute hissy fit over flower girls. The convert family (on both sides) hadn't thought to ask if it was permitted, and the priest only found out about the flower girls when they arrived at the rehearsal. The flower girls (two sister) were the daughters of a non-Orthodox relative of the groom, and the kids parents were treated extremely rudely by the priest.
Some Greek parishes in the US have organs, which can be used for music before/after the wedding. I'm not in favor of such. I was at a wedding last summer in a Greek parish with an organ, and it really altered the experience of the wedding for me. All previous weddings I've attended have been in OCA parishes (I've SUNG them at myself) or Antiochian. No organ!
OP, if your fiance is attending a Greek parish, then the witnesses will have to be Orthodox - in good standing with the Church. I mention Greek parish because I've found those to be stricter (going off statements on their websites) than some OCA or Antiochian parishes, for example. Actually, the Greek tradition has a koumbaro, which is pretty much like a godparent for a marriage, rather than just one sponsor. I don't know if two are permitted.
Also, are you aware that Sunday after Liturgy is the accepted time for Orthodox weddings? Depending on the bishop, you might or might not be able to get permission for a Saturday wedding earlier in the day (no evening wedding).
Also, the Orthodox Church has restrictions on days when weddings can be held. Lots of days are out that would be fine in another Christian body.
Don't make any plans or ask anyone to be in your wedding without finding out what the priest expects.
Below is a link to the wedding section of a Greek parish in my area. It appears to be fairly standard.http://www.stjohnthebaptistgoc.org/worship/sacraments/weddings