As I'm sure you're all aware dates can be a thing of conflict and fusion; but to get to William Oliver (which ever ones they/he pan out to be) may i lead you along my tree briefly.
My great great Grandfather was George Oliver b Swinton circa 1842 who married Jane Nettleton whose father was John Nettleton, Smithy living at Rotherham around 1865. My lineage is baffling but suffice to say two of George's sons had a part, one blood the other marriage in my line. All searchable on line (I use Latter Day Saints as it has the most info for free).
George's father was also George, b Swinton circa 1800. Records I found on line say 1804, but a newly found relative who has scrutinised many documents from this time suggests 1800. The online records I obtained show age at residences etc that compute to 04, but given some people's ages are approximate in official records as give or take 4 or 5 years the actual person is likely to be the same.
He married Ann - my searches have yet to find a surname but new relly gives us Gregson. He seemingly also had sons John Thomas and Samuel but I have found so much out lately I can't keep up. On searchable records I found parents for him called William and Mary. I think this might be a baptism not birth) at Middleton Tyas though i have no reason as to why that place, nor indeed why not.
William Oliver according to records I've been given married Mary Turner at Wickersley in 1782. Searchable records again show a couple of William Olivers births that would tie in. It is now that I stumble across a William Oliver staying with the Shaws and I hope to attach, a document to this post. Given the dizzying mess I'm in I cannot say if this is at all relevant, but given how much of my ancestors fit together despite erroneous data I tend to think their in before I rule them out. I hpe this at least eliminates an issue for you if it doesn't unearth one you missed.
I find that a google search with a date or the same with a spouse or whoever can bring surprises.
Cannot save to this pc (normally use Apple) so will try to paste here (ps it does not show occupations by pasting - Shaws were potters as were various Olivers, though I understand William was also a tailor:
William Oliver Census 1841
Name William Oliver
Place Wath Upon Dearne, Yorkshire,Yorkshire West Riding, England
Residence Swinton
Aged 80-84
born 1761-1765
Birth County County Yorkshire
Town Rotherham
Book Number 11
Parish Wath Upon Dearne
County Yorkshire,Yorkshire West Riding
Page Number 11
Registration Number HO107
Piece/Folio 1329/25
Household
Thomas Shaw M 35-39 Yorkshire
Elizabeth Shaw F 40-44 Yorkshire
Ann Shaw F 15-19 Yorkshire
William Shaw M 12 Yorkshire
Alfred Shaw M 7 Yorkshire
William Oliver M 80-84 Yorkshire
England and Wales Census, 1841
Line Number 15
Digital Folder Number 101721298
Image Number 00494