I am saving 3 different file sizes of PNG's (1" x 2", 2" x 3", 3" x 4"). When I place them all in Indesign or MS Word they are all the same size. All of them show up in their folder as different sizes. Why is this?
There's a few important factors here:
In Photoshop, the zoom level is linked to the pixel dimensions of the file. If Photoshop says it's zoomed to 100%, that means one pixel in the file is being displayed as one pixel on your display.
In InDesign, because it's predominately a print design app, images are placed so that the PPI is respected. InDesign assumes the display you're using is 72PPI (which almost certainly won't be correct, but ignore that for now), so an image that's 72PPI will appear the same size in Photoshop at 100% zoom as InDesign at 100% zoom.
I have no idea what Word does. It's probably like InDesign, because that's how most print-centric apps work.
It depends what your final goal is, but getting the images to appear at the correct size in InDesign and Word should be fairly easy. If you're printing, you probably want the images to show as the correct physical size in Image Size under the Image menu in Photoshop, with Pixels/Inch set to 300PPI. If you're sending the Word doc to people for on screen use only, you may want it to be far lower.
Additional info: PNG files typically store pixel density as PPM (pixels per metre), so you can't actually save files at 300PPI — rounding errors turn those into 299.999PPI.