I think re-signing Chychrun who has spent his career on bad teams should be the top priority. He hasn't been on a Playoff team in 5 years. He'll only be 27 at the start of next season so even an 8 year deal would only take him to age 34. He's tied in Points with Carlson who may be gone in the next couple years. Chychrun has 17 Goals, the rest of the defense has combined for only 12.
The Backstrom and Oshie contracts are off the books completely after this season. Mangiapane, Eller, Raddysh, Vrana, Dowd and Lindgren are all UFA. Dowd and Lindgren are the only 2 of that bunch I'd look to bring back as the rest could be replaced with cheaper in-house options like Leonard, Miroschnichenko, Lapierre and Trineyev.
If they make deadline moves, I don't expect anything big. The chemistry of the team is the ultimate strength. Even on a 3 game losing streak (for the 1st time all season) I think they should stand pat unless they can upgrade 3C without giving up too much.