Cracknell, 30, has played 44 games for the Vancouver Canucks this season, scoring five times with five assists in a bottom-six role.
Pardy, 31, has played 14 games for the Winnipeg Jets, registering one assist while logging an average of 13:06 of ice time.
Both Cracknell and Pardy are pending unrestricted free agents. Their additions may signal more moves for the Oilers, be they trades or demotions.
On Saturday, Edmonton traded d-man Justin Schultz to Pittsburgh for a third-round draft pick. That left the Oilers with just six defensemen on their active roster. Hardy makes it seven.