Eastwood started his football career with Southend as a member of their youth squad from 1997 to 1999. In 1999, he moved to West Ham's youth academy and signed his first professional contract with the Hammers in 2002. He was released in 2003, having failed to make any League appearances.
He signed with non-League side Grays Athletic for the 2003-04 season, and became the club's top scorer that season with 37 goals. In October 2004, he returned on loan to Southend, then in League Two.
In that first match, he headed home a cross in 7.7 seconds, a League record for a debut (but behind the overall record of 3.5 seconds set by Barrow's Colin Cowperthwaite against Kettering Town in 1979). Eastwood scored his second in the 58th minute, then his third in the 87th minute.
Eastwood left Southend after the 2006-07 season, having scored 49 league goals in 111 appearances, but returned in 2012 and played another two seasons there.