Moncur, 23, turned down the chance to join Posh this summer to move to the Tykes from Colchester for a fee believed to be about £500,000.
But he has made two appearances for Barnsley so far and has been allowed to leave on loan.
Neither McGee or Oduwa, both 20 have made a Spurs first-team appearance.
However, Oduwa has had loans at Luton, Rangers and Colchester, while McGee comes in following the release of keeper Ben Alnwick from his Posh contract because of "family and geographical reasons".
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Peterborough have signed Barnsley midfielder George Moncur and Tottenham goalkeeper Luke McGee and winger Nathan Oduwa on loan until January.