Here is a script which collates the data and produces the desired compact view:

#! perl
use strict;
use warnings;
use feature 'switch';

{
    my %h;
    populate  (\%h);
    stringify (\%h);
    print_view(\%h);
}

sub populate
{
    my ($h) = @_;

    while (<DATA>)
    {
        my ($date, $type, $word) = split /\s+\|\s+/;
        chomp $word;

        unless (exists $h->{$date})
        {
            $h->{$date}{woody_words} = [];
            $h->{$date}{tinny_words} = [];
        }

        given ($type)
        {
            when ('woody') { push @{ $h->{$date}{woody_words} }, $word
+; }
            when ('tinny') { push @{ $h->{$date}{tinny_words} }, $word
+; }
            default        { warn "Datum '$word' of unknown type '$typ
+e'"; }
        }
    }
}

sub stringify
{
    my ($h) = @_;

    for (keys %$h)
    {
        $h->{$_}{woody_str} = join(', ', sort @{ $h->{$_}{woody_words}
+ });
        $h->{$_}{tinny_str} = join(', ', sort @{ $h->{$_}{tinny_words}
+ });
    }
}

sub print_view
{
    my ($h)  = @_;
    my  $max = 0;

    for (keys %$h)
    {
        my $woody_str  = $h->{$_}{woody_str};
        my $new_length = length  $woody_str;
        $max = $new_length if defined $woody_str && $new_length > $max
+;
    }

    printf "   date      | %-*s | tinny words\n", $max, 'woody words';
    printf "-------------+-%s-+-------------\n",  '-' x $max;
    printf "%s  %-*s   %s\n", $_, $max, $h->{$_}{woody_str}, $h->{$_}{
+tinny_str}
        for sort { cmp_dates() } keys %$h;
}

{
    my %months;

    BEGIN
    {
        %months = (Jan =>  1, Feb =>  2, Mar =>  3, Apr =>  4,
                   May =>  5, Jun =>  6, Jul =>  7, Aug =>  8,
                   Sep =>  9, Oct => 10, Nov => 11, Dec => 12);
    }

    sub cmp_dates
    {
        my ($day_a, $mon_a) = $a =~ /^(\d{1,2}) (\w{3})/;
        my ($day_b, $mon_b) = $b =~ /^(\d{1,2}) (\w{3})/;

        return ($months{$mon_a} < $months{$mon_b}) ? -1 :
               ($months{$mon_a} > $months{$mon_b}) ? +1 :
               ($day_a          < $day_b)          ? -1 :
               ($day_a          > $day_b)          ? +1 : 0;
    }
}

__DATA__
28 Sep (Fri) | woody | caribou
28 Sep (Fri) | tinny | litterbin
29 Sep (Sat) | woody | wasp
29 Sep (Sat) | woody | yowling
29 Sep (Sat) | woody | gorn
30 Sep (Sun) | woody | intercourse
30 Sep (Sun) | woody | bound
30 Sep (Sun) | woody | pert
30 Sep (Sun) | tinny | newspaper
01 Oct (Mon) | woody | ocelot
01 Oct (Mon) | woody | concubine
01 Oct (Mon) | tinny | antelope
02 Oct (Tue) | woody | vole
02 Oct (Tue) | woody | sausage
03 Oct (Wed) | tinny | recidivist
03 Oct (Wed) | tinny | tit
[download]

Output:

23:09 >perl 345_SoPW.pl
   date      | woody words              | tinny words
-------------+--------------------------+-------------
28 Sep (Fri)  caribou                    litterbin
29 Sep (Sat)  gorn, wasp, yowling
30 Sep (Sun)  bound, intercourse, pert   newspaper
01 Oct (Mon)  concubine, ocelot          antelope
02 Oct (Tue)  sausage, vole
03 Oct (Wed)                             recidivist, tit

23:10 >
[download]

Of course, the really interesting question is: How do you distinguish words which are ‘woody’ from those which are ‘tinny’?  ;-)

Hope this helps,

Updates: Minor code improvements.