The latter: some kind of algorithm or rather a transform of each weekday into a new name which is alphabetically sorted right (as per the %order or whatever calendar order). For example, transform each weekday by removing the 1st letter, then their cmp order is correct. OK this does not work. But I was looking for this kind of transform. Of course I can try exhaustively find such transform with random masks on the weekday bytes.

monday:011011010110111101101110011001000110000101111001
tuesday:01110100011101010110010101110011011001000110000101111001
wednesday:011101110110010101100100011011100110010101110011011001000110
+000101111001
thursday:0111010001101000011101010111001001110011011001000110000101111
+001
friday:011001100111001001101001011001000110000101111001
saturday:0111001101100001011101000111010101110010011001000110000101111
+001
sunday:011100110111010101101110011001000110000101111001
[download]

(with this:

for (qw/monday tuesday wednesday thursday friday saturday sunday/){
 print $_ .':'. join('', map { sprintf "%08b", ord($_) } split(//, lc 
+$_))."\n";
}
[download]

Honestly, I find those magical formulas° always too voodoo.

From a maintenance point of view they are horrible, because they don't scale well with new requirements.

Even Doomsday fails if you go back before Gregorian calendar

Cheers Rolf
_{(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery}

°) don't know the correct term here... ³

update

there is only a limited number of orders 7!

so you could try a brute force search composing formulas based on inputs like substrings or word-length.

I'm still not sure if the solution will be shorter than just a clever list.²

update

²) tybaldt's solution with "motuwethfrsasu" is just an example of such a clever list.

³) kind of golfing, isn't it?