All three have featured in Kettering's pre-season games.
Central midfielder Barker, 24, started his career at Leyton Orient before spending time at Cheltenham Town and also had loan spells with Wingate & Finchley and Northwood.
He joined Braintree Town in August 2019 from Haringey Borough, where he was a regular in the North London's successful side.
Prior to his spell at White Hart Lane, he moved to Isthmian Premier outfit Potters Bar Town in February 2020 and then to Bishop`s Stortford in July 2021 but then signed for St Neots Town at the end of that month.
In July 2022 he moved to Isthmian North outfit Bury Town.
Forward O’Keefe has joined the Poppies from League One neighbours Northampton Town having previously been a member of their under-19 side.
Leicester-born, the 18-year-old joined the Cobblers as an under-15.
He had a `work experience` spell last season with then-Northern Premier League Division One Midlands outfit Daventry Town.
He has impressed during pre-season and has snapped up by ready for the new campaign.
Reilly returns to Latimer Park after ending the 2022/23 season on loan with new league rivals Redditch United.
The 26-year-old had originally joined Kettering in August 2022 from Banbury United.
He had been with the Puritans since August 2021 after arriving from Daventry Town.
He had signed for the Motormen in early October 2020 from Stratford Town, who he had only joined in August 2020 after a spell playing football in the United States.
Coventry-born, he attended the University of Rio Grande and played for the Red Storm.
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