TextEdit will paste text without formatting or links if you first go to the Format menu and choose the Make Plain Text command.
This will lose all formatting, including alignment and justification. It sounds like you don't want to do this; it sounds like you want to preserve SOME formatting (like justification) and get rid of some other formatting (like links).
Word can do this if you hit Paste, then click on the weird little symbol you see at the end of the text you paste and choose "Match Destination Formatting" or "Keep Text Only". (The little symbol--it looks a bit like a crude drawing of a clipboard--is actually a popup menu. It disappears as soon as you start to type again.)
