Greenrod is a rather unusual surname, so unusual that I can well imagine it being mistranscribed as Greenwood many times.
However the 3 sources you showed me all to my mind show
I have found a record for a Mary and an Agnes Greenrod in Philadelphia in 1862. I think it stretches the odds a little to believe that there were 2 unrelated families of Greenrods in circulation in Philadelphia in the mid 19th century. The record shows Agnes and Mary Greenrod joining St David´s Protestant Episcopal Church in Manayunk, Philadelphia, Pennsylvania. Manayunk is a neighbourhood in the North west of the city nowadays although how it stood vis a presumably smaller 19th century Phily I don't know.
Anyway the record is conveniently on ancestry at:http://search.ancestry.co.uk/cgi-bin/sse.dll?rank=1&new=...
This seemingly contradicts the Greenwood evidence and the 1876 migration, but the previous writer is correct, you have to be prepared to chase some dead ends sometimes and at the very least having some leads to chase is better than just running up against a brick wall with no particular ideas what to do next.
In terms of the migration record from 1876, the first questions I would have would be, who is she travelling with and where from? where is she going to?