Javascript, 169 characters
(not counting unnecessary line breaks and indentation)
Edit: Now with input permutation
o=" ";i=i.split(o);z="+-*/";for(y=0;y<27;y++)for(x=0;x<16;x++){a=y/9|0;b=(y/3|0)%3;c=y%3;if(a!=b&&a!=c&&b!=c){s=i[a]+z[x/4|0]+i[b]+z[x%4]+i[c];o+=s+"="+~~(eval(s)+.5);}}
With indentation:
o=" ";
i=i.split(o);
z="+-*/";
for(y=0;y<27;y++)
for(x=0;x<16;x++)
{
a=y/9|0;
b=(y/3|0)%3;
c=y%3;
if(a!=b&&a!=c&&b!=c)
{
s=i[a]+z[x/4|0]+i[b]+z[x%4]+i[c];
o+=s+"="+~~(eval(s)+.5);
}
}