my @digits = split //, abs;
with:
my @digits = split //, $_;

##</code><code>##

C:\_32\pscrpt>perl try.pl
Argument "-" isn't numeric in addition (+) at try.pl line 10.
Argument "-" isn't numeric in addition (+) at try.pl line 10.
Argument "-" isn't numeric in addition (+) at try.pl line 10.
-221 -21 1 1 3 5 21 34 89 144

##</code><code>##

no warnings 'numeric';

##</code><code>##

sub oddDigitSum {
    no warnings 'numeric';
    my @ans;
    for(@_) {
        my @digits = split //, $_;
        my $sum;
        $sum += $_ for @digits;
        $sum % 2 && push @ans, $_;
    }
    return @ans;
}