The Thunder were eliminated in 6 games by the Mavericks in the first round. I'm a bit late on this one but here's how their offseason is shaping up:

Cap Space

Contracts

Draft Picks

1st Round The Thunder will have the 12th pick in the draft this year (via Houston).

2nd Round

Outlook

The Thunder had a breakout season this year and surprised everyone by grabbing the 1 seed in a tough Western Conference and Shai was a finalist in MVP voting. They looked set to have a deep post season run but ended up losing to the Mavs in 6. With the Mavs being 1 step away from being in the finals the Thunders loss to them doesn't seem as bad so the Thunder will likely have at least the 2nd round as their goal for next season given the leap they made this year.

The Thunder will go into the offseason with near max cap space (Proj. $35M-$37M) due to most of the team outside of Shai being on Rookie/Cheap deals. In addition to the cap space they have the most coveted stock of draft picks in the NBA. This gives them a lot of flexibility to make a move if they feel one is needed this early.

While disappointing to go out in the first round as the 1 seed, the Thunder have one of the brightest futures in the NBA given the success they had this season, having numerous picks, and some cap flexibility to make further improvements to their roster to push for a deeper post season run next season.

Source