According to this link, the admission records for Strabane workhouse exist for the years 1862 – 1921. The records are in PRONI (the public record office) in Belfast. They are not on-line so a personal visit is required to view them. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
PRONI is closed at present due to Covid but hopefully will re-open in the next few months.