There are a couple of family trees on this line on Ancestry. They have some details on both William and George, along with some other siblings. They show both William and George returning to Scotland after their Irish marriages.
William and wife Mary Ann Margaret Murphy in the 1871 census - everyone showing as born in Ireland except for William Snr.:
William Oman 46, Working Jeweller b. Edinburgh
Margaret Oman 40 b. Ireland
Goerge Oman 18
Agnes Oman 15
William Oman 12
Frances Oman 4
Margaret Oman 6 months
Address: 12 Shilong Square, Glasgow
William's death shows on 12/07/1892 in St Cuthbert's Poorhouse, Edinburgh. You should be able to confirm this yourself on www.scotlandspeople.gov.uk. His parents are given as John Oman and Agnes Haig.