Are you able to look at the records Oldohiohome?
Just thinking, if you can, without too much trouble, then they might be a better chance to find William's parents?
Helen
Shellyesq and Sandra both have access to ancestry's US records, from what I have seen, and familysearch online is free once you register.
I did find this record at the Oak Hill Cemetery site:
Abslom Johnson, burial # 2010, age 5, died August 20, 1862, cause of death: inflammation of bowels, Dr Runcie
he was in William's household in 1860.
and Jane Stitt's burial:
Jane Johnson, age 38, born Ireland, died November 9, 1858, cause of death: chronic diarrhoea, Dr G B Walker
section 8, lot 43
Regarding William's parents - I know Johnson is a very common name but if you have both Absolom and William in the same county in the US in 1850s and it looks like William has Absolom's children with him in 1860, then I'd take that as enough evidence that they were brothers. 
There is a tree at ancestry that says they are half-brothers, but it didn't look very reliable. You'd have to find the English records to be sure.
They weren't from Cambridgeshire by any chance? I think a few families from there settled in Evansville.