How can I copy/paste multiple key-frames in After Effects from different layers?
There is no way to copy-n-paste keyframes from multiple layers without using a script.

You can show the keyframes in a layer by hitting the u key. And then you can copy those keys layer by layer.

I'm not sure why you're opposed to using a script. I wrote one that can copy and paste keys from multiple layers in a single click (including copy-pasting with time reversal), and which is free and open source, you can download it here.