James Mullen [assumed to be an error and should be Joseph], age 37, born in Ireland, teamster, separated from wife
son: James Mullen, age 8, born in Oregon
son: Alfred Mullen, age 6, born in Oregon
daughter: Mary A Mullen, age 4, born in Oregon
There is a note after each child saying "with Father". Since the children are also listed with their mother in Clover Creek, Baker, Oregon in the same census (see Mary Jane Westfall's page), either they moved from her household to his between the dates the 2 census records were taken (hers 9-14 June, his 29 June), or the note is an error and should have said "with Mother". Apparently the children were living with him by 1884, so the former explanation is possible.
The fact that G. E. Mullen is not included in the list of Joseph's children could mean that he wasn't Joseph's son, or (more likely, given the lack of other information about him) that he had died by 1880. Edward is also not listed here, but is in Joseph's will, so was probably his son and too young to be living with him.