The duo impressed while on trial with the Latics, and both players have now penned one-year deals.
Left-back Steer, 19, spent three months on loan at Gillingham last season while also making one substitute appearance for the Gunners against Burnley in the Carling Cup.
Ojapah, also 19, is a central midfielder who manager Penney believes can have a huge impact at Boundary Park.
He told the club's official website: "This youngster has got what it takes but there is still a long way to go. Philip needs to buckle down and work hard now."