The Hurricanes traded Wood to the Red Wings in exchange for Oliwer Kaski on Thursday.
The Devils waived Wood for the purpose of assignment to AHL Binghamton on Monday, Stephen Whyno of the Associated Press reports.
The Sharks traded Wood to the Hurricanes in exchange for Trevor Carrick on Tuesday.
Wood re-signed with the Sharks on a one-year, two-way contract with San Jose on Thursday which will pay him $700,000 at the NHL level, CapFriendly reports.
The Sharks extended Wood a qualifying offer Tuesday.
The Coyotes traded Wood to the Sharks in exchange for Adam Helewka on Thursday.
Wood is an option for the Coyotes, who have lost the highly touted defenseman Jakob Chychrun to a knee injury for an indefinite period of time, Arizona Sports reports.
Wood signed a three-year, entry-level contract with the Coyotes on Wednesday.
Wood was sent to the Coyotes along with Alex Tanguay and Conner Bleackley on Monday for Mikkel Boedker, Renaud Lavoie of TVA Sports reports.
Avalanche coach Patrick Roy confirmed Wood would miss training camp due to a wrist injury, Mike Chambers of the Denver Post reports.