You have to painstakingly try to figure out the format and then do the conversion:
update ignore data
set pdate = (case when oldDate rlike '[12][0-9]{3}-[0-1][0-9]-[0-3][0-9]'
then str_to_date(oldDate, '%Y-%m-%d')
. . .
end)
Doesn't sound like fun. But, having inconsistent data in a column is even worse.