You might want to look at some Merge components as what you describe is exactly what Merge tools do between the common base, version control file and local file. Except that you want more than 2 files (+ base)...
Just my $0.02
Try Scooter Software's Beyond Compare. It supports 3-way merge and is written in Delphi / Kylix for multi-platform support. I've used it pretty extensively (even over a VPN) and it's performed well.
for f in file1 file2 file3 file4 file5; do echo "$f\n\n">> outF; diff $f baseFile >> outF; echo "\n\n">> outF; done
SourceGear Diffmerge is nice (and free) for windows based file diffing.
I made my own diff tool DirDiff because I didn't want parts that match two times on screen, and differing parts above eachother for easy comparison. You could use it in directory-mode on a directory with an equal number of copies of the base file. It doesn't render exports of diff's, but I'll list it as a feature request.
None of the existing diff/merge tools will do what you want. Based on your sample screenshot you're looking for an algorithm that performs alignments over multiple files and gives appropriate weights based on line similarity.
The first issue is weighting the alignment based on line similarity. Most popular alignment algorithms, including the one used by GNU diff, TDiff, and TrmDiff, do an alignment based on line hashes, and just check whether the lines match exactly or not. You can pre-process the lines to remove whitespace or change everything to lower-case, but that's it. Add, remove, or change a letter and the alignment things the entire line is different. Any alignment of different lines at that point is purely accidental.
Beyond Compare does take line similarity into account, but it really only works for 2-way comparisons. Compare It! also has some sort of similarity algorithm, but it also limited to 2-way comparisons. It can slow down the comparison dramatically, and I'm not aware of any other component or program, commercial or open source, that even tries.
The other issue is that you also want a multi-file comparison. That means either running the 2-way diff algorithm a bunch of times and stitching the results together or finding an algorithm that does multiple alignments at once.
Stitching will be difficult: your sample shows that the original file can have missing lines, so you'd need to compare every file to every other file to get the a bunch of alignments, and then you'd need to work out the best way to match those alignments up. A naive stitching algorithm is pretty easy to do, but it will get messed up by trivial matches (blank lines for example).
There are research papers that cover aligning multiple sequences at once, but they're usually focused on DNA comparisons, you'd definitely have to code it up yourself. Wikipedia covers a lot of the basics, then you'd probably need to switch to Google Scholar.
I know this is an old thread but vimdiff does (almost) exactly what you're looking for with the added advantage of being able to edit the files right from the diff perspective.