Blackwood, who was recalled from the AHL after the Kinkaid trade, was 6-4-0 in 13 games with New Jersey earlier this season.
Ottawa receives prospects Vitaly Abramov and Jonathan Davidsson, a first-round pick and another first-rounder if Duchene re-signs in Columbus.
The NHL trade deadline is Monday, but some teams already have made some splashes.
The additions come at a time the Blue Jackets have won seven of 10 and jumped into third place of the Metropolitan Division standings, a point ahead of Pittsburgh, which is now ninth and out of the playoff picture.
The Rangers had obtained him in a trade on September 11, sending Steven Kampfer, a fourth-round pick and a conditional seventh-round pick to the Bruins, with whom he won the Stanley Cup in 2011.
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"We're pleased with the futures we've received in this deal", said Senators general manager Pierre Dorion. Both will be unrestricted free agents by the end of the season.
Dzingel has 22 goals and 22 assists in 57 games this season for the last-place Senators.
Together, Duchene and Dzingel shared the ice for over 500 minutes in Ottawa. The Blue Jackets now have six players with over 20 goals scored this year on the roster and don't count out the captain Nick Foligno with 15 goals scored currently.
Meanwhile Ottawa can now focus its attention entirely on the most important asset under its label in the lead-up to Monday's trade deadline.
The 26-year-old Weal has four goals and seven assists in 47 games this season.
The undrafted free agent played his best in the second half of last season, taking over for an injured Schneider and leading the Devils to their first playoff spot since reaching the Stanley Cup Finals in 2012. "We've had plenty, but nothing that would make us trade him".