Seeking a linen weaver

I am seeking anything about my ancestors in Ireland.  The information I know is as follows:

My 4x great grandfather, James Hart (b. abt 1784) married Mary Crawford.  They had eleven children all said to be born in Tyrone, Ireland.  Of those children, one child, Elizabeth Hart who married a William Walker and stayed in Ireland.  The remaining children went to Vaughan, York, Ontario, Canada.  The family immigrated in 1846 to the Ontario area.  It is found on an old family tree that this family was at Castlefinn - Strabane and Donegal.   When looking at a map from 1820, it makes some sense with exception of the counties.  It may help to have the children's names, Elizabeth, Samuel, Thomas, William, Robert, Mary Jane, Margret, John, May, and James.  Of these children, I have much information on most, but cannot locate Elizabeth (walker) Hart.   Most importantly, I would like some information that says this family was really in Ireland.  I also know the family was Presbyterian.  James (1784) was a linen weaver, Samuel was a shoemaker, William was a farmer.    Samuel married Christine Malloy in Ontario, William married Isabella Cunningham, also in Ontario.