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The former football league player has made appearances for Bolton Wanderers, Milton Keynes Dons, Coventry City, Wigan Athletic and Blackpool.
The 26-year-old joins on a deal until January from Halifax Town.
“It’s a good situation to come into, but at the same time the boys are winning so it’s not like I expect to be thrown straight into the team," Odelusi told the club's official website.
“It doesn’t happen like that in football.
“I want to work hard to prove that I deserve a starting place.”
South Shields currently lead the way in the BetVictor Northern Premier League table, with seven wins and 22 points.
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