Midfielder Elsom was at West Ham United as a youngster.
He had spells with Tilbury and Histon and was also with Bishop`s Stortford.
His first spell with Great Wakering came two years ago before returning this season following a short time at Ware.
Striker Mignot arrives at Barking from another league rival, Grays Athletic.
He moved to the Blues in the summer from West Essex.
Mignot proved himself to be one of the most clinical strikers in the Essex Senior League last season, as he notched 30 goals in 41 games for West Essex, helping them to secure a seventh-place finish.
That form saw the striker finish as the third highest scorer in the division, leading to him being named in the Essex Senior League’s team-of-the-season.
But he failed to reproduce his best form at Grays, with 2 goals in 10 appearances, only three of which were starts.
Defender Willis arrives at Mayesbrook Park from Canvey Island.
The 21-year-old signed for the Gulls from Tilbury in August and has also played for Great Wakering and Basildon United.
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