I want to get rid of a closet wall. It's odd shaped, so figured we open the room up. It's on the 2nd floor, no basement. The 1st floor doesn't have a wall under it.
How can I tell whether this wall is (or was) load bearing?
These walls are almost certainly not. That's the extent of confidence anyone here can provide. Either assume the risk of removal or consult a local expert.
You cannot tell just from a photo like this. You need to check above and below and see if there is any load on this wall. If in doubt, you should consult an engineer or architect.
That being said, this would be a relatively unusual place and shape for a load bearing wall but if it is and if you remove it, the integrity of your home may be compromised. So at least do the checks in the attic and in the basement or crawlspace to verify it's not supporting anything.