Carson, 20, moved to Anfield from Leeds in January 2005 for £750,000 and has made nine appearances for the Reds.
Bischoff, 24, has been troubled with injuries but he completed the whole game in City's reserve's 4-2 win over Wigan on Thursday.
Both players go straight into the Owls squad to face QPR at the weekend.
Sturrock said: "Scott is an exciting keeper and a great prospect.
"I've watched Mikel from afar and am very excited with him. He was outstanding on loan at Wolves.
"The financial commitment has come from the chairman. He's made it plain he did not want to the club's debts and any wages would come out of his pocket."
news.bbc.co.uk/sport2/hi/football/teams/s/sheff_wed/4794486.stm
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