Is it normal for trades to happen between eliminated teams while the playoffs are ongoing or is this just a product of COVID?
Teams were always permitted to do business (trades/signings) during the playoffs, but typically there wasn't much urgency to do so until it gets closer to the draft. As I understand it, Covid actually limited things this time as only eliminated teams were allowed to make trades.
Typically trades will revolve around unsigned prospects whose rights would expire on June 1st. Occasionally there'd be a more familiar NHL name.
Quick scan since 2000:
May 1, 2000: Kings acquired Steve Passmore from Chicago for a 4th round pick (possibly expansion draft related)
May 23, 2000: Ducks traded unsigned prospect Trent Hunter to the Islanders for a 4th round pick (Anaheim would have lost his rights on June 1)
May 31, 2001: Vancouver acquired rights to (unsigned?) goalie prospect Alex Auld from Florida for 2nd and 3rd round picks (Panthers had a young Roberto Luongo fall into their laps the previous offseason).
June 12, 2002: Philadelphia traded Brian Boucher and a 3rd rounder to Phoenix for Michal Handzus and Robert Esche (the Stanley Cup Final concluded the next day)
May 28, 2003: Kings acquired Roman Cechmanek from Philadelphia for a future 2nd round pick.
May 15, 2007: Boston acquired unsigned draft choice Adam McQuaid from Columbus for a 5th round pick (which eventually became Jamie Benn)
June 4, 2008: Kings traded T.J. Fast to the Blues for a future 5th round pick.
May 13, 2010: Coyotes traded unsigned Jared Staal to the Hurricanes for a 5th round pick (I don't think Phoenix was intending to sign him). Couple more unsigned guys in Jyri Niemi and Mattias Modig were traded before the June 1 deadline that year.
May 8, 2011: Coyotes traded prospect forward Oscar Lindberg to the Rangers for prospect forward Ethan Werek. Werek was a mid-2nd rounder in 2009, but I don't think the Rangers were going to offer him a deal.
June 4, 2012: Penguins acquired the rights to impending UFA Tomas Vokoun from Washington for a 7th round pick.
May 25, 2016: Vancouver acquired Erik Gudbranson from Florida for Jared McCann and a 2nd rounder
April 28, 2017: Chicago traded the rights to impending free agent goalie Scott Darling to Carolina for a 3rd round pick.
May 9, 2017: Kings traded the rights to impending free agent goalie Ben Bishop to Dallas for a 4th round pick. Kings also acquired Boko Imama on the eve of the signing deadline that year.
May 3, 2018: Carolina traded Marcus Kruger to Arizona for Jordan Martinook.
April 30, 2019: Carolina traded unsigned prospect Adam Fox to the Rangers for a pair of 2nd round picks (Fox could have played out his senior year and signed with the Rangers in 2020.)