I seem to recall another posting here not long ago about the Kilturra area, so you might look for that to see whether it has any helpful info. Kilturra is the name of both a civil parish (an administrative district), and a townland within that civil parish. You can see more info about the civil parish here, and will see a link there to info about the townland.
Kilturra is in the Catholic parish of Kilshalvey, which straddles the border of Mayo and Sligo. The parish records which are available online can be found at this site:
Those records go back to the 1840's for baptisms, and earlier for marriages, so you may be able to find baptismal records for Patrick and Honoria there (looking in the 1845-55 time frame would be my guess, because people married pretty young in East Mayo). That would take you back another generation. You should also be able to find a marriage record for them, assuming that Honoria was from the same parish (weddings usually took place in the bride's parish).
Kilshalvey lies mostly in Sligo, and that is an area where the border was changed in the 1800's, so it may be that the part of Kilshalvey which is now in Mayo was formerly in Sligo.
All of the chldrenn you listed were born after the start of civil registration of births in 1864, so there should be birth records online for them. There's another contributor here who has ready access to a database with such records, so he will probably be able to answer that for you.