Hide this storage space over stairs

You could probably alter a sheet that would go with your décor to fit the opening, or if you don't have plants for the wall, you could just hang it down to the length of the tallest part of the opening. With a sheet, you could get by with hanging smaller rods, perhaps with command hooks since the sheet is so light. That way you wouldn't have to put holes in your wall. I hope that gives you another idea to think about, Lisa!

Unfortunately this triangle of space is very inefficient and does not lend itself well to hanging up clothes. I would concentrate first on trying to reconfigure it to better meet your closet needs, before spending any money trying to cover it up. What is behind the lower triangular portion that is drywalled? Might building in some shelves or sliders be a possibility?

You could you add pull out drawers instead of hanging things? Essentially this pic in reverse?

Wow. I would love to meet the architect that designed this building. And how it was passed in building inspections. Even in a studio, you need a decent closet or space for your belongings. If hacking into what looks to possibly be a stairwell(?) is not an option, I would go with some sort of curtain. And I would use a plastic backed curtain at that. Since it shares space with kitchenette, if you saute onions and garlic, your clothes will smell like that too as it will permeate the area. Hope you have a window to open or a fan. In my world not a bad thing, but many might not find that pleasant. Is there any space to utilize in the sleeping area?

Could you put a sliding barn door?

personally, I would see about installing one or two shelves. The triangular bottom section can hold shoes or boots. To cover over the entire area, I would most likely just use a shower curtain or drapes. If plan to leave open, I would paint wall and use left over paint on some Rubbermaid bins to match/blend.

If you just want to hide this, what about installing used shutters?