First of all, that isn't your code -- here's what perltidy and the Perl compiler would like it to be:

#!/usr/bin/perl -w

use strict;

{
    my $a    = 20;
    my $b    = 22.5;
    my $c    = 23;
    my $atob = $a - $b;
    my $btoc = $b - $c;
    my $atoc = $a - $c;
    my @matrixflags;

    if ((($atob > 1) || ($atob < -1)) && (($atoc > 1) ||     
         ($atoc < -1))
          && (($btoc > 1) || ($btoc < -1)))
    {
        print OUTFILE "DIFF > 1 all three\n";
        $matrixflags[$row - 4][$i] = 1;
        $matrixflags[$row - 3][$i] = 1;
        $matrixflags[$row - 2][$i] = 1;
    } elsif ((($atob > 1) || ($atob < -1)) && (($btoc < 1)   
           && ($btoc > -1))
          && (($atoc > 1) || ($atoc < -1)))
    {
        print OUTFILE "DIFFA > 1 $atob  $atoc $btoc\n";
        $matrixflags[$row - 4][$i] = 1;
        $matrixflags[$row - 3][$i] = 0;
        $matrixflags[$row - 2][$i] = 0;
    } elsif ((($atob > 1) || ($atob < -1)) && (($btoc > 1) 
           || ($btoc < -1))
          && (($atoc < 1) && ($atoc > -1)))
    {
        print OUTFILE "DIFFB > 1 $atob  $atoc $btoc\n";
        $matrixflags[$row - 4][$i] = 0;
        $matrixflags[$row - 3][$i] = 1;
        $matrixflags[$row - 2][$i] = 0;
    } elsif ((($atob < 1) && ($atob > -1)) && (($btoc > 1) 
           || ($btoc < -1))
          && (($atoc > 1) || ($atoc < -1)))
    {
        print OUTFILE "DIFFC > 1 $atob  $atoc $btoc\n";
        $matrixflags[$row - 4][$i] = 0;
        $matrixflags[$row - 3][$i] = 0;
        $matrixflags[$row - 2][$i] = 1;
    }

    #So in this example in my head the 1st elsif should be executed.
    #Difference $atob = 1.5 so (($atob > 1) || ($atob < -1)) is true.
    #Difference $btoc = 0.5 so (($btoc < 1) && ($btoc > -1)) is true.
    #Difference $atoc = 3 so (($atoc > 1) || ($atoc < -1)) is true.
}
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Secondly, even that throws errors -- neither $row or $i are defined (either using my or programmatically). Why not show us a fragment of code that at least compiles and runs, then we'll be able to help you.