Probably you don't want grep, but instead map and a regular expression substitution (see perlretut and perlre):

use strict;
use warnings;

my @call = (
    'A19284 hostname 07/09/07 moredata moredata',
    'A19384 hostname 06/09/07 moredata moredata',
    'A19234 hostname 07/08/07 moredata moredata',
    );
my @callClean = map {$_->[1]}
    sort {$a->[0] cmp $b->[0]}
    map {[(join '', @{[split '/', $_->[0]]}[2, 1, 0]), $_->[1]]}
    map {m|^\w+\s+(.*?(\d+/\d+/\d+).*)|; [$2, $1]} @call;

print "$_\n" for @call;
print "$_\n" for @callClean;
[download]

Prints:

A19284 hostname 05/09/07 moredata moredata
A19384 hostname 06/09/07 moredata moredata
A19234 hostname 08/08/07 moredata moredata
hostname 08/08/07 moredata moredata
hostname 05/09/07 moredata moredata
hostname 06/09/07 moredata moredata
[download]

Update: sort by the dates too.