If I understand you correctly, here is the solution:
use strict;
my ($A,$B,$C)=([1,2,4],[1,2,2],[1,2,3]);
my @outer=($A,$B,$C);
my @sorted=sort { $a->[0] <=> $b->[0] ||
$a->[1] <=> $b->[1] ||
$a->[2] <=> $b->[2] } @outer;
map { print "@$_\n"; } @sorted;