So, the kind of EVA foam I used is just craft foam, the kind you can get at Joann's or Michael's. You can get it much thicker, 1/2" or more (available at big hardware stores) and there are wonderful tutorials showing how to use it, but the thin kind was just what I needed for this project. And it's much easier to work with.
The photo above shows the wings for Thor's helmet before painting. Let me show you how I did this.
I used the craft foam glue that is sold by the same company that makes the foam, but any contact cement works.
The areas that are going to be glued to the cloth part of the helmet need to be kept free of paint. Because my original plan was to use spray paint, I masked these areas off with painter's masking tape. If you are a careful hand painter this tape isn't needed.
BUT, I found out spray paint doesn't work AT ALL. It's super messy and just kept soaking in and in and in, never really sealing off the surface.
The thing to use is GESSO or MODGE PODGE.