What materials do I need to fix these walls? (not even sure if it's actually drywall)
Yes that is just drywall with joint compound.

To start you should secure the corner bead (the metal strip), just a screw in the hole nearest the open corner will suffice.

If there is any more loose joint compound or paint scrape it off now.

Then you can put spread new joint compound over the holes and the corner bead. When its dry, sand. You will probably need two coats to get it smooth.

This is a very easy repair and rather cheap. You can buy one of the small buckets of joint compound such as this one. At the cheapest a plastic putty knife (lowes link) (I'd get a proper metal one. You will use it again, and it is also good for scraping). 

Last thing is just to prime and paint. (the painting will be the most expensive part).