Taylor, 30, started his career with the Latics, making 254 league appearances before joining Millwall in May 2012.
Former Bolton winger Obedayi, 27, scored two goals in 25 appearances for the Scottish Championship side.
He has also played under Oldham boss John Sheridan, having served under him at Chesterfield and Plymouth Argyle.
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Oldham have re-signed Bolton winger Chris Taylor on loan until the end of the season and brought in Tope Obedayi after his release by Dundee United.