The other part you didn't add is that they are all super aggressive. Eloy's walk rate this year was back down to where it was during his rookie year, so he's not getting on base. Vaughn's walk rate was bad and it got worse during the year, he had a 2 month period from July to August where he had 3 walks. There is some reason to believe that decent coaching could help these guys improve, but the White Sox are specifically picking coaches who want their guys to hit the ball on the ground and be aggressive, so you see that as a reason why these guys are bad, the White Sox want them to do this.
I do think there's a decent chance someone would take on most of Eloy's contract if you were trying to clear the money. I would be ok with clearing that deal, but it's not a big move that improves them.
Vaughn will be in his first arbitration season this year. There's no good reason to move him yet, he'll get paid like $2 million, his trade value is zero, and there's no one around pushing for 1b. For a rebuilding team with no real path to competing like the White Sox, there's no reason not to hold onto him for 1 more year, even if he has a 1/100 shot of breaking out, that's better than the chances you'd have if you played Sheets there.