I have found a Robert Oakman, who was born in Ireland, is working as a Bricklayer in Philadelphia in 1860. He is living with wife Margaret and children: Robert, Margaret, Mary and Martha. Their eldest child, who was 9 in 1860, was born in Pennsylvania so Robert must have arrived in the US prior to 1851.
What happened to this family beyond 1860 is a mystery! They don’t turn up in any of the later US Censuses. Perhaps they returned to Ireland, or moved on to some other country entirely.
At first I thought this was the Robert who arrived on the Sea King in 1848, but as there is a 10 year discrepancy in ages this is unlikely … though not impossible. Both Margarets were born in Ireland and they were both the same age. I am keeping an open mind on this possibility.