Imad was part of the Notts side that won the trophy in 2020 and returns for a third spell at Trent Bridge ahead of their final two group games, and potentially the knockouts beyond.
Notts sit fourth in the North Group and will qualify for the quarter-finals if they win either of their remaining games, both of which are at home: against Birmingham Bears on Friday, then Leicestershire on Sunday.
"We're delighted to welcome Imad back, particularly with the memories we have with him lifting the trophy at Edgbaston three years ago," Peter Moores, Nottinghamshire's head coach, said. "We have two big games at Trent Bridge with qualification in our own hands and an opportunity to still gain a home draw depending how other results go."
Sodhi will act as cover for Peter Siddle (hand), Roelof van der Merwe (finger), Lewis Gregory (finger) and Lewis Goldsworthy (rib) who are all sidelined through recent injuries.
"Everyone is aware of the injuries that we have picked up to senior players over the last week or so," Andy Hurry, Somerset's director of cricket, said. "It was imperative at such a key stage of the Vitality Blast campaign that we acted quickly and identified a player who could add real value to our squad."