"I went to watch Eddie for the Watford youth team and reserves, and he stood out each time," boss Justin Edinburgh told the club's website.
"I'm sure he will be a good addition to our squad."
Oshodi went on loan to Dagenham & Redbridge in November but never played for them.
Meanwhile, Diamonds' Kurt Robinson has left the club for Chelmsford City, following his loan spell at the Blue Square Bet South side.
The 21-year-old made 71 appearances for the club after joining in 2009.
Source: BBC Sport
Source: BBC Sport