Jake Odorizzi gets activated today to face the Royals, filling out the 28-man active roster which will include 16 (!) pitchers. The way the Twins are playing it, they need all or almost all of those pitching slots because they have had a grand total of four six-inning starts at this point in the season. Further, more length won't be expected soon from Rich Hill or Odorizzi as they come off the IL, nor from Thorpe or Smeltzer as they fill in until the rotation has some semblance of stability.
With the activation of Odorizzi, the Twins will have starters Hill and Bailey and reliever Zack Littell on the IL. Josh Donaldson was put on the IL yesterday and has to be on the shelf for at least a week. Also, Willians Astudillo is still on the IL, but has been in St. Paul for 12 days. I would presume he is close to being physically ready to join the team.
General managing from my couch, I would expect that the Twins drop a pitcher sometime before Donaldson returns, but really I don't see them going any lower than 14 pitchers for the rest of the season. Among the pitchers, I would guess the activation progression would be Littell, then Hill and finally Bailey. As I understand it "Dick Mountain" is expected to throw a bullpen while on the road trip and could be activated when the team gets back home. Littell can come off Monday, I believe and he figures to be totally healthy by then.
So, who goes when these guys return? I think Poppen is the first choice to be sent back, given that his option has been used already and that he is the last guy in the 'pen. Next would probably be one of Thorpe or Smeltzer--Thorpe perhaps getting another start in the coming days. Alcala or Thielbar would probably be options if all are healthy and the team want "only" 15 arms.
As far as the position players go, I don't know when but the club has to decide on Astudillo pretty soon. I assume he has options, so if Avila and Garver stay healthy, the Turtle might get optioned to St. Paul. If not, I would presume that when Astudillo is activated, the club will cut back by one pitcher, unless someone else comes up injured. Donaldson's return would probably prompt a return to 14 position players, although by then, someone else will probably have a disabling injury.
I think the Twins, by virtue of the versatility of Gonzalez and Adrianza, are well suited to play with fewer position players, even with 16 pitchers, they have major league depth at all positions.
My educated guesses will probably all be wrong and almost certainly in the next couple of weeks, new injuries will be added to the mix. It is interesting to see how Derek and Thad manage the active roster and 40-man.