What is the best way to get cut open plastic to stick to other pieces?
There's a website specifically about adhesives, ThisToThat.com. It probably can recommend not just a type but brands. I have artist friends who swear by its information.
Soda bottles are made from PET (polyethylene) plastic which is almost like Teflon....almost nothing sticks to it. Here are some solutions that Permabond recommends: https://www.permabond.com/materials_bonded/4508/ You didn't state what you're trying to construct, so it's hard to make recommendations. Since you mentioned staples, it may be that it doesn't matter how the bond looks...as long as it holds the sheets together. One solution would be to overlay the pieces and use a hammer and nail to punch holes. Then sew the joint together using clear fishing line or strong twine. If you do opt to use adhesives, you'll probably need to clamp the joint. You *can* use your C-clamps for this. Get a couple of wood blocks that will span the distance, and clamp them at the ends.
try heating it with a iron, it may adhere together with heat
Others I'd consider using are duct tape/military tape, glue gun, super glue etc
Hard to get acrylic powder for nails of late