I had to read your description a few times to see that your question wasn't what BrowserUK answered. Given the arrays you list above, try something like this:

my %A;
for (0..$#A_v_B1) {
  $A{$A_v_B1[$_]}{B} = $A_v_B2[$_];
}
for (0..$#A_v_C1) {
  $A{$A_v_C1[$_]}{C} = $A_v_C2[$_];
}
[download]

That will give you a hash A that looks like this:

  A101 => { B => B302, C => C302 },
  A103 => { B => B405 },
  A104 => { B => B406 },
  A106 => { C => C305 },
  A109 => { C => C306 },
[download]

From there, you can see what elements of A have matches in which other sets, and what those matches are. You can build up hashes for B, C, and D similarly, if needed.