Central midfielder McKnight signed towards the end of last season and won the club’s Goal of the Season award.
Goalkeeper Oldham is an academy product and will work with Nick Culkin and Cameron Belford, who Radcliffe recently signed from Nuneaton Borough following the end of his loan spell at FC United.
As well as Belford, manager Lee Fowler has already brought in Kole Hall, Jonathan Royle and Jo Cummings.
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