They're still a bit bulky, but much neater with this quick one-material trick.
All you need are rubber bands. (Finally, justifying my compulsive saving of produce rubber bands for the last two years.)
Neatly stack a bunch of hangers*. Loop a rubber band around all the hooks, wrap under the hypotenuse of the hangers, and loop back over one or more of the hooks.
Don't over-stretch the rubber bands; adding explosive power to your hangers only exacerbates the packing problem. If your rubber bands aren't long enough, you can just chain** more on until it reaches.
Now you have some solid 3D triangles, they should fit more neatly into a box or bag. And, if you're short on space, you can stuff small or soft things into the triangles' centers. They can even serve as a protective box around something fragile.
*Pro tip: figure out the height of the bag or box you're going to pack them in. Then measure the height of the hangers. Make your stacks of hangers (or some multiple thereof) match the height of the container.
**Chain rubber bands like hair ties: poke one through the other, then feed the other end of the loop through the poked-through end and pull. Should look like a lark's head knot. If you've never done this before, just fiddle around with a couple of rubber bands until you get it.