This is an interesting discussion of funeral practices.
Most of the Lutheran funerals I have been to here in South Carolina have been ECLA funerals. They have been straight out of LBW and uses its order for the Burial of the Dead. I actually like that service very much, with its emphasis on the baptism of the deceased and its stress on the resurrection. I have not seen much eulogizing of the dead down here, other than a few personal remarks that the pastor might make before the funeral service starts.
I have not been to any LCMS, WELS, or other Lutheran funerals here or anywhere else.
In the Orthodox Church, we don't have normally have any funeral sermons, although I suppose a priest could preach one if he wanted to. There is no requirement for it. When someone dies, we do the following:
1. Serve the First Panikhída (Memorial Service) at the place of death (usually at the hospital with just the priest and the family members present). This is done in the hospital room itself immediately after death before the body is taken to the morgue. It is a short service.
2. Serve the Second Panikhida (Memorial Service): This is usually done in the evening at the funeral home, after family, relatives and friends have come to pay their respect to the deceased. The church choir will usually come to sing at the Panikida at this service. It is also a rather short service.
3. Serve the Third Panikhida (Memorial Service): This takes place in the nave of the parish church and takes place in the morning, sometime before noon. The Psalter is chanted over the deceased as soon as the body is brought into the church. Often, but not always, if the body is brought over the night before, people may volunteer to keep vigil at the coffin and take turns reading the Psalter. (That is really kind of optional and it is not required, but is a custom many people like to do to show their respect to the deceased.) Then the actual funeral service begins at the time appointed and it takes the form of a Matins service, with an Epistle and a Gospel Reading added. At the end of the service the priest approaches the coffin (which was open for the entire service) and offers a prayer of absolution for the sins of the deceased. Then the people are invited to come forward and give the deceased the Last Kiss. (Again, if someone isn't comfortable with it, they aren't forced to.) Then the lid is put on the coffin, and it is carried out to the hearse.
When the hearse arrives at the place of burial it is carried out and carried to the grave while "Holy God, Holy Mighty, Holy Immortal" is sung. The priest says a brief prayer, the coffin is lowered into the grave, and all present cast dirt on it. Then they fill up the grave with dirt while everyone stands there. When they are finished the priest says "This tomb is sealed until the Second Coming of our Lord, God and Savior, Jesus Christ."
Then people usually gather somewhere and enjoy a memorial meal in memory of the deceased.
There really is no tradition of a "Requiem Mass" in Orthodoxy. If it is desired to celebrate the Divine Liturgy, it takes place in the Church on the morning of the funeral and it precedes the Third Panikhida service. Usually, though, it is omitted and it is in no way required.