I noticed this neighbour in Kilstrule, who might be related (she was in the adjacent house):
And in 1911:
Sarah Wilson (senior) died 29.8.1904 at Kilstrule, aged 55. Her death certificate states she was a spinster. The 1901 census does describe her as a widower but it’s possible she may never have married. Her daughter Sarah was the informant and would presumably have a fair idea of the situation.
I found a likely birth for Charles on 27.8.1882, registered in Strabane.
Likewise for Sarah Margaret on 18.9.1883. The informant was Maggy who I suspect was the Marjorie in the 1901 census. (Maggie and Marjorie are interchangeable). So they might be sisters.
Both births were illegitimate, as suggested by the 1904 death certificate for their mother.
https://churchrecords.irishgenealogy.ie/churchrecords/ (Search under civil records).
I had a look for Robert’s birth but could not find it but presumably it too was illegitimate. You might want to keep searching. Try leaving the forename box blank as not every child was named when the birth was registered.
A father’s name only appears on an illegitimate child’s birth cert if he is present at the registration and confirms paternity. (Otherwise anyone might be named with obvious difficulties later).
You could have a look at the church baptism records. Assuming the children were baptised, the record sometimes says who the reputed father was. The births appear to be in the parish of Ardstraw, and the family were Church of Ireland. There are 3 churches in that parish. I do not know the area well enough to say which of the 3 the family are likely to have attended. Ardstraw itself has records from 1882, Baronscourt 1877 & Drumclamph 1877. All 3 did have earlier records which were sent to Dublin for safekeeping but ironically were destroyed in the Public Record Office in the 1922 fire, during the civil war. So you might not find a baptism for Robert but you should find Charles and Sarah.
There’s a copy of the surviving church records in PRONI (the public record office) in Belfast. They are not on-line and a personal visit is required to view them.
If the parents weren't married, you may struggle to get any information about the children's father Robert. It's such a common name that I see no easy way of distinguishing him from others in the area. (Assuming he was still alive and in Tyrone, there were 54 people named Robert Wilson in the county in the 1901 census).