I read the name as Mary Jane GREENROD. I think that the various permutations possible make this the most likely.
In cases like this I write down a story of everything I know and the questions that arise. Its normally a number of pages but from what you've given us it starts something like this:
About 1857 Mary Jane GREENROD (GREENHOD, list options) is born. Where was she born? Did she grow up in England or in the USA? We have no record of her family however she married in the USA so would have travelled to the USA sometime between 1857 and 1876 where she married Augustus REESE. Were any witnesses given to the marriage? Were any of these from her family name? If not, I would try a hypothesis that she travelled out the USA without her family or they had died at this point. I would explore death records for GREENRODS in the parish where she married. If none are found I would explore the possibility she travelled alone - thus would have been older before leaving. On this theory, she would appear in one of the English Censuses prior to 1878.
I tested this theory and found a possible match. This is just a theory, remember. Now I ask: IS this Mary Jane GREENRAD my ancestor? You can see if you can follow her tracks a bit more... look for her in the 1871 Census... does a Mary Jane GREENRAD (possibly a misspelling of GREENROD) marry in England - if its the same one she is not the right one and you try again. Maybe she came out with her siblings. ... see if there are any GREENRAD / RODS in Philadelphia... etc etc. How about witnesses on the certificates you have? Any BOSTON's?
Name: Mary Jane Greenrad
Estimated Birth Year: abt 1858
Mother's Name: Mary Ann Greenrad
Where born: Manchester, Lancashire, England
Civil Parish: Manchester
Ecclesiastical parish: Collegiate
Registration District: Manchester
Sub-registration District: Market Street
ED, institution, or vessel: 17
Neighbors: View others on page
Household Schedule Number: 144
Page Number: 28
Thomas Boston 72
Amelia Boston 21
Mary Ann Greenrad 23
Joseph Greenrad 4
Mary Jane Greenrad 3
Edward Greenrad 16
Harriet Blaney 22http://search.ancestry.com/cgi-bin/sse.dll?db=uki1861&in...
Anyway, this iterative hypothesis and test method is the way I have solved various brick walls involving immigrant families.
Another option is to search for ANY GREENRODS in Philadelphia. Doing this, I located this record for Joseph GREENROD who died, aged two, in 1863. Interestingly, his parents are given as GRINDROD...
Father: Robert Grindrod
Mother: Martha Grindrodhttp://search.ancestry.com/cgi-bin/sse.dll?rank=1&new=1&...
I would be exploring the theory that she was a GREENROD born in England but whose name was originally GRINDROD...
A cursory search of Ancestry shows that most GRINDROD's originated in Lancashire. I would then resume my search for GRINDRODS / GREENRODS in Lancashire ... trying to match up the family with any other GREENRODS you have as likely family in Philadelphia.
Document your searches and document any Mary Jane GREENROD / GRINDROD's you eliminate through death elsewhere, marriage elsewhere etc. You will eventually find a clue that will match to one of your hypothetical Mary Jane's and you will then write up your discovery and explain why you believe she is the one!
Good luck and have fun.