I've forwarded this post to OrthodoxHistory.org, with hopes that somebody may be able to identify the priest, and from there possibly be able to identify who were the people in the pictures.

Funny how people's attitudes change. The comments on here show that post-mortem photography is considered macabre by todays standards, yet when this picture was taken it was still acceptable. I myself have taken pictures of many family members and close friends in their caskets, although I would not feel right if they were displayed.
http://en.wikipedia.org/wiki/Post-mortem_photography
A photo of a recently deceased celebrity on a tabloid cover caused a minor uproar, but a century ago the same picture would likely have been run on the front page of respectable newspapers.
As for the guy in the box, he looks dead tired.

Greek, to be more precise, I believe.
Russian/Slavonic rite has been the three-barred cross for a long time, and the Maltese cross has in-tapered ends, compared to the square ends of the Greek cross.

Studying the clergyman I am going to guess Eastern Orthodox Christians: The beard was not common in the 1920's but orthodox would accept it; the collar does not seem to be Roman rite; and the cross on the priest's stole seems to fit the Eastern tradition.

He looks a lot older in person.

accomplished what the embalmer could not!

OK, he never looked so good.

AntonioB almost nailed it: I worked with press photographers who made money on the side shooting funerals like this. They were taken for the people left behind in "the old country," wherever that might be. Most commonly they were shot in a hall, with everyone seated around the casket. Pro tip: without fail, all those sitting would have their hands on their knees, clearly showing that they had all (or most) of their fingers, to calm those "back home" that the dangerous factories where they worked hadn't gotten them - yet.

Looks like a funeral in my familia. Although mine were Northern Italians. These look to be Sicilian.

Or do we just push it into the ground?

He's packed in there very nicely. It could be a long, rough trip, and he won't get damaged.

I'm guessing that it was a very warm day seeing as how the makeup is melting off the corpse.

One of my favorite regulars on the Ed Sullivan show was
Senor Wences. For some reason this shot reminded me of him. 's alright? 's alright.

No doubt at all that at least one guy in this photo is dead today.

I couldn't sleep so I thought I'd get up and look at a little Shorpy. Geez! What a nightcap...won't sleep now....what was that noise?????

probably because it beats looking at the creepy dead guy!

I have no words for how disturbing this is. Possibly it's because I dislike open coffins, but this is freaky.

Gah. The guy's left eye and mouth appear to be slightly open. Last look around is right!

Also, from the pic, I thought it was a reusable coffin with a door at the bottom that would let the dearly departed slip out into an open hole like they do for burials at sea.