If your date is right then you should be able to find the birth certificate for Mary Ellen Ryan Meehan from here (cost about £7)
http://www.1837online.com/Trace2web/
This should yield an address in Accrington, and from this (if they didn't move around too much) you may get a little more detail from 1861 Census. The 1861 Census may just say born Ireland, which would not help too much, but would yield a little more about the occupation of parents, and may identify siblings and/or other family members.
There is always a risk that they were not living at the address shown on Mary's birth certificate in 1861.
I am not sure I have come across St Oswald's Parish, not sure if someone else could help here.
For Irish research you may wish to check out Cyndi's list here
http://www.cyndislist.com/ireland.htm
Good luck