Something like the following:

    Map[Sort[#] &, list]
    (*{{{a, 1}, {b, 3}, {c, 5}}, {{a, 5}, {b, 1}, {c, 3}}, {{a, 5}, {b, 3}, {c, 1}}, {{a, 1}, {b, 5}, {c, 3}}}*)

Your problem in general is somewhat complicated for more characters, but I will think a little more about it.