You need to detect the end of each individual file, print your results for that file and reset the counts. See the explanation of eof(ARGV) in perlfunc:

#!C:\Perl
use strict;
BEGIN{
    @ARGV=map glob, @ARGV;
}
open(RES, ">>results.txt");
print RES "File Number    A    A%    B    B%    Null    Null%\n";
my $A = 0; #these three lines set my initial counts at zero
my $B = 0;
my $null = 0;
my $filenum = 0;

while( <> ){
    chomp($_);
    if ($_ eq "stringa"){
        $A++;}
    elsif ($_ eq "stringb"){
        $B++;}
    else {
        $null++;
    }
    if( eof( ARGV ) ) { ## true after the end of each individual file
        my $popa = sprintf( '%.2f', $A / 1000 ); 
        my $popb = sprintf( '%.2f', $B / 1000 );
        my $popnull = sprintf( '%.2f', $null / 1000 );
        my $filenum++;  #Add one to my filenumber

        print RES "$filenum        $A    $popa    $B    $popb    $null
+    $popnull\n"; 
        $A = $B = $null = 0; ## Reset counts for the next file
    }
}
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As I mentioned above, if OS/X is a *nix-like system, you probably don't need the @ARGV = map glob, @ARGV as the shell will take care of that for you. (Though it probably won't do any harm.)

Also, in your code you have several place where you do:

...
my $var = ....;
my $var = sprintf ... $var;
...
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If you are running with strict and warnings, you should be getting messages of the form: "my" variable $var masks earlier declaration in same scope at .......don't ignore them, they are there for a purpose.