Massey, 22, has signed until 2017, while 22-year-old Eastman has agreed a deal until 2016 and Kent, 18, will stay with the League One side until 2018.
All three have featured prominently this term, with teenager Kent making his first senior start in August.
"It's been a long journey to get to where I am and I can't thank everyone enough," he told BBC Essex.
"I'm feeling comfortable in the team and I'm getting used to my surroundings.
"Once I started playing a few games I think the club wanted to reward me. I couldn't turn it down - I love playing here."
Young U's midfielder Sammie Smzodics also signed a contract until 2018 last week.
Colchester United have handed new deals to striker Gavin Massey and defenders Tom Eastman and Frankie Kent.