OK, here is what I found.

Journal files are indeed stored in
/sdcard/.edge/.esi-content
and have extension .esj

These files appear to be xournal files, but you cannot open them with xournal. You need to do the following first:
copy foo.esj to another machine with xournal installed.
mv foo.esj foo.gz
unzip foo.gz

Then open foo with text editor, and replace line
<page width="396.00" height="540.00" tabname="">
with line
<page width="396.00" height="540.00">

Then do:
gzip foo
mv foo.gz foo.xoj

The resulting foo.xoj file can then be opened with xournal. I guess I will simply write a script which does this automatically.