I am probably to late to be of any help, but I can add one significant detail. I find the logic more intuitive if we initialize the result with a large negative number. You can get the largest possible number from POSIX, but with only a small loss in generality, we can choose any number that is larger than any we expect in our input.

se strict;
use warnings;
#use POSIX qw(DBL_MAX);
my $x = $ARGV[0] // -11;
my $y = $ARGV[1] // -13;
my $z = $ARGV[2] // -17;
#my $MAX_NEG = -DBL_MAX;
my $MAX_NEG = -99999;      # Better to use DBL_MAX from POSIX
my $max = $MAX_NEG;

if ( $x % 2) {
    $max = $x ;
}
if ( $y % 2 and $y > $max ) {
    $max = $y ;
}
if ( $z % 2 and $z > $max ) {
    $max = $z ;
}
die "There are no odd values.\n" if ($max == $MAX_NEG) ;
print "the largest odd number is $max.\n";
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Note: I took the freedom to use the disallowed operator (//) to override the default values of $x, $y, and $z with values from the command line. I do not consider this part of the solution.