Code:
https://www.offalyhistory.com/family-history
This non-profit site helps people trace families in Offaly county. It might be worth asking them for some help, because they have access to local records. Although Fancroft and Shinrone are close to Birr (and are all in Offaly county) and the Oxley surname does seem to be Hawksley, which is an unusual name in Ireland, I agree with you that the fact that George Oxley was born c1796, and is living with a sister Mary born c1810, decreases the likelihood that there is any connection with the John Hawksley who lived in Orr (from at least 1799) and who until his retirement in 1817 served in the artillery in Ireland and Canada. My guess is that John Hawksley was sent to Ireland in 1798 during the Irish rebellion.
It does not rule it out however, because the ages on the Census can be out by a couple of years, as is the case with John Hawksley, who is listed as born c1773 when he was actually born in 1771. What I have done is prove that he is the John Hawksley who was born in Yorkshire, and that he had families in both Ireland and Canada. It is possible that he had more than one family in Ireland (given his history!!!) but the only way to prove it (one way or another) is to take an Ancestry DNA test, because some of his descendants have taken the test.