From what I can tell, "Etch-O-Matic stencils are essentially the impregnated blue paper stencil material (like carbon paper from days of old) that you use with an old manual typewriter or a dot matrix printer. Please understand that "dot matrix printer" means one of the ancient printers that used inked ribbons and connected to computers by way of serial or parallel ports. Modern computers do not have those ports any more, so it is all but impossible to drive a dot matrix printer, even if you can find one at a junk store or a yard sale. Again, you have to understand that inkjet and laser printers won't work.
So that just leaves old manual typewriters. I will say that you can still buy old manual typewriters. You just can't be sure they will do anything useful with the stencil material. I bought one for just this purpose. It is a right royal pain in the backside to get a usable stencil from it. I do it from time to time to do things like marking the steel type, or inscribing my name on the spine or such like. It's not really a good way to go. Doesn't look very professional, and you are limited to using the font of the typewriter (unless you get an IBM Selectric with multiple font balls).
Oh, by the way, the stencil material is very fragile. I never got more than one use from a stencil. Removing it tore it to pieces.