Find Ancestors

I am trying to find out information about my Grandmother's parents, John Johnson and Elizabeth Leviston. My grandmother (Violet Elizabeth Johnson) was born on Cookstown, Co. Tyrone in 1915 and was the youngest of three children (the other two were Mary and John and were considerably older than her - Mary was born c.1894). Her parents were a Catholic and Protestant couple who had married and therefore been cast out by their families. Sadly Catherine died when my grandmother was a baby (aged c.40) and John died around a year after so Violet was then cared for by her sister Mary. Unfortunately I don't know if they came from the Co Tyrone area or moved there to get away from their families. I do know that they spent some time in Scotland as Mary's death cert states that she was born there. John (Jnr) married and had a daughter called Kathleen (whose married name was Kathleen Gallagher) who emigrated in the 60s to Australia and then NZ. If anyone has any clues, I would be very very grateful - I would love to know more about this story. Many thanks!