First, you have a selection problem, so you use a grep. Let's not grep the values themselves but the index for each item:

my @input_numbers = (1, 2, 4, 8, 16, 32, 64);
my @indices_of_odd_digit_sums = grep {
  ...
} 0..$#input_numbers;

Here, the expression 0..$#input_numbers will be a list of indices for the array. Inside the block, $_ is a small integer, from 0 to 6 (seven items total). Now, you don't want to decide whether $_ has an odd digit sum. You want to know whether the array element at that index has an odd digit sum. Instead of using $_ to get the number of interest, use $input_numbers[$_]:

my @indices_of_odd_digit_sums = grep {
  my $number = $input_numbers[$_];
  my $sum;
  $sum += $_ for split //, $number;
  $sum % 2;
} 0..$#input_numbers;

The result will be the indices at which 1, 16, and 32 appear in the list: 0, 4, and 5. You could use these indices in an array slice to get the original values again:

my @odd_digit_sums = @input_numbers[ @indices_of_odd_digit_sums ];

The strategy here for an indirect grep or map is to think of the $_ values as identifying a particular item of interest, such as the key in a hash or the index of an array, and then use that identification within the block or expression to access the actual values.

Here's another example: select the elements of @x that are larger than the corresponding value in @y. Again, you'll use the indices of @x as your $_ items:

my @bigger_indices = grep {
  if ($_ > $#y or $x[$_] > $y[$_]) {
    1; # yes, select it
  } else {
    0; # no, don't select it
  }
} 0..$#x;
my @bigger = @x[@bigger_indices];

However, this is a bit more verbose than it needs to be. You could simply return the boolean expression rather than a separate 1 or 0:

my @bigger_indices = grep {
  $_ > $#y or $x[$_] > $y[$_];
} 0..$#x;
my @bigger = @x[@bigger_indices];

my @bigger = map {
  if ($_ > $#y or $x[$_] > $y[$_]) {
    $x[$_];
  } else {
    ( );
  }
} 0..$#x;