Make your various $sql definitions into an array.

Make an array the has $pointer will use.

Make an array of references to the arrays you'll push.

The you have (with lots of room for exercises for the user)

my $dbh = DBI->connect("DBI:ODBC:$db",$user,$pass,{RaiseError => 1});
my $sth;
my @sql = .....;
my @ptr = .....;
my @arr = .....;

for my $idx ( 0..$#sql )
  {
    $sth = $dbh->prepare( $sql[$idx] );
    $sth->execute() || die $sth->errstr;

    while ($pointer = $sth->fetchrow_hashref)
      {
        $value = $pointer->$ptr[$idx];
        $value =~ s/\s+$//g;
        push $arr[$idx], $value;
      }
  }
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One array of a structure would be better than several arrays, but yoiu get the idea.