Forward Duffy-Weekes began his career at Barnet before joining Welwyn Garden City and Havant & Waterlooville. He has also featured for Stamford Lions.
Goalkeeper Logan, 34, started his career at Leicester City, and has gone on to appear for Boston United, Rochdale, Hibernian and Mansfield Town.
Central defender Stainfield joins the club from Newark FC, and has previously featured for Spalding United, Gainsborough Trinity and Boston United.
The Pitching In Northern Premier League S/East Division side face Hereford on Saturday 16 against Hereford in the fourth round of the FA Trophy, with the club live streaming the fixture for free.