>>I would guess that "SS Caledonia" maybe has something to do with identifying a church, I'm not conversant with saints' names, but I have (for example) seen "SS" to indicate two saints names connected with a church. Perhaps these are two nuns/priests/parish employees?<<
1) Trinity Church is Episcopal, no nuns or saints. You weren't kidding when you say you're not conversant.
2) SS Caledonia was an immigrant vessel. This inclusion in a marriage record of this detail most likely means they were all very recent immigrants at the time of the marriage.