Hit F6 to open the Object Editor, you can export all sorts of stuff there, just click a tab and use the Export entries in the File menu to export things, import to bring them back in.
You can also export it all at once, but then importing it will overwrite everything.
If you need to move imported files like artwork, use WinMPQ to extract and then re-add them (use Add Folder to do it fast). Just be warned it doesn't always work, as in sometimes you'll add a bunch of files and they won't all wind up in the map, so you'll have to do them by hand in the Import Manager.