Is it possible to ask git diff to include untracked files in its diff output, or is my best bet to use git add on the newly created files and the existing files I have edited, then use:
git diff --cached
With recent git versions you can git add -N the file (or --intent-to-add), which adds a zero-length blob to the index at that location. The upshot is that your "untracked" file now becomes a modification to add all the content to this zero-length file, and that shows up in the "git diff" output.
git diff
echo "this is a new file" > new.txt
git diff
git add -N new.txt
git diff
diff --git a/new.txt b/new.txt
index e69de29..3b2aed8 100644
--- a/new.txt
+++ b/new.txt
@@ -0,0 +1 @@
+this is a new file
Sadly, as pointed out, you can't git stash while you have an --intent-to-add file pending like this. Although if you need to stash, you just add the new files and then stash them. Or you can use the emulation workaround:
git update-index --add --cacheinfo \
100644 e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 new.txt
(setting up an alias is your friend here).