...September 21-23, 1994 we will be hosting visitors...

...submissions should be made by 11 February 1994...

...Mail sent 7 Feb 1994...

...On the 16th September 1994 Mr X will be giving a talk on ...

...unconfirmed conference dates are March 4, 5 and 6, 1994...

(...is MY emphasis - for clarity's sake)
Have absolutely no knowledge of surrounding boundaries, nor where the strings can occur in the text, just got to pull them all out, so that I can then do some date normalisation...also, i've found that some of my strings are sometimes matching numeric strings...

Here's my attempt. I've used two regexes for the general cases of day month and month day.

#!/usr/bin/perl

use strict;
use warnings;

while (<DATA>){
  if ( # month day
    /
      (
        [JFMASOND][a-z]{2,8} # full or 3 letter month name
        \s
        [123]?\d             # day number
        (?:-[123]?\d)?       # optional dash and day number
        (?:,\s[123]?\d\s)*   # optional list of day numbers
        (?:and\s)?           # optional and
        (?:[123]?\d,?\s)?    # optional end of list
        (?:19|20)\d{2}       # year starting 19 or 20
      )
    /x
  )
  {
    print "1: $1\n";
  }
  elsif ( # day month
    /
      (
        [123]?\d                # day number
        (?:st|nd|rd|th)?        # optional st, nd etc.
        \s+
        [JFMASOND][a-z]{2,8}    # month name
        \s+                     
        (?:19|20)\d{2}          # year starting 19 or 20
      )
    /x
  )
  {
    print "2: $1\n";
  }
}
__DATA__
...the next social club meeting is on April 15, 1994...
...September 21-23, 1994 we will be hosting visitors...
...submissions should be made by 11 February 1994...
...Mail sent 7 Feb 1994...
...On the 16th September 1994 Mr X will be giving a talk on ...
...unconfirmed conference dates are March 4, 5 and 6, 1994...
[download]

output:

---------- Capture Output ----------
> "C:\Perl\bin\perl.exe" _new.pl
1: April 15, 1994
1: September 21-23, 1994
2: 11 February 1994
2: 7 Feb 1994
2: 16th September 1994
1: March 4, 5 and 6, 1994

> Terminated with exit code 0.
[download]

Here I start by checking if there's a valid month name in the string. If there is, I start extracting the dates from the string; else skipt that line.
Note that I had to add a space after the first '...' because '...September' is not a valid month name.
Updated to return valid dates

#!/usr/bin/perl
# filename: extract_dates.pl

use strict;
use warnings;
use Data::Dumper;
$Data::Dumper::Indent = 1;

my @dates;
push @dates, findMonth($_) while (<DATA>); 
print Dumper \@dates; # or do something else with your dates

sub findMonth {

    my @words = split / /,shift;

    my %months = map {$_ => 1 } qw/
        january jan february feb march     mar
        april   apr may      may june      jun
        july    jul august   aug september sep
        october oct november nov december  dec
    /;

    foreach (@words) {
        if (exists $months{lc($_)} ) {
            return extractDate(
                {
                    MONTH  => $_,
                    STRING => "@words"
                }
            );
            last;
        }
    }

    return;

}

sub extractDate {

    my $self = shift;

    return makeValidDate(
        {STRING=>$self->{STRING},DATE=>$1}
    ) if ($self->{STRING} =~ 
        /
        (
            (?:
                (
                    [123]?\d
                    (st|nd|rd|th)?
                    \s+
                )?
                $self->{MONTH}
                \s\d{1,4}
                (
                    (-[123]?\d)?
                    (,\s[123]?\d\s)*
                    (and\s\d+)?
                    (,\s\d{4})?
                )?
            )
        )
        /x
    );
    
    return;

}

sub makeValidDate {

    my $self = shift;
    my ($string) = $self->{STRING} =~/^(.+)$/;

    $self->{DATE} =~s/-/X/g;
    $self->{DATE} =~s/(^-|\W|and|th|st|nd|rd)/ /gi;
    
    my @date = split /\s+/,$self->{DATE};
    my $date = {};

    foreach (@date) {

        if ($_=~/^\d{1,2}$/) {
            push @{$date->{days}},$_
        } elsif ($_=~/^\d{4}$/) {
            $date->{year} = $_
        } elsif ($_=~/(\d+)X(\d+)/) {
            push @{$date->{days}},$1 .. $2
        } else {
            $date->{month} = lc($_)
        }

    }

    use Date::Manip;
    my $out_date = {};
    
    foreach (@{$date->{days}}) {

        my $temp_date = ParseDate(
            $_ . " "
            . $date->{month} . " "
            . $date->{year}
        );

        $temp_date = &UnixDate($temp_date,"%D");
        push @{$out_date->{dates}},$temp_date;
        $out_date->{string} = $string;
    }

    return $out_date;

}

__DATA__
... the next social club meeting is on April 15, 1994...
... September 21-23, 1994 we will be hosting visitors...
... submissions should be made by 11 February 1994...
... Mail sent 7 Feb 1994...
... On the 16th September 1994 Mr X will be giving a talk on ...
... unconfirmed conference dates are March 4, 5 and 6, 1994...
[download]

$VAR1 = [
  {
    'dates' => [
      '04/15/94'
    ],
    'string' => '... the next social club meeting is on April 15, 1994
+...'
  },
  {
    'dates' => [
      '09/21/94',
      '09/22/94',
      '09/23/94'
    ],
    'string' => '... September 21-23, 1994 we will be hosting visitors
+...'
  },
  {
    'dates' => [
      '02/11/94'
    ],
    'string' => '... submissions should be made by 11 February 1994...
+'
  },
  {
    'dates' => [
      '02/07/94'
    ],
    'string' => '... Mail sent 7 Feb 1994...'
  },
  {
    'dates' => [
      '09/16/94'
    ],
    'string' => '... On the 16th September 1994 Mr X will be giving a 
+talk on ...'
  },
  {
    'dates' => [
      '03/04/94',
      '03/05/94',
      '03/06/94'
    ],
    'string' => '... unconfirmed conference dates are March 4, 5 and 6
+, 1994...'
  }
];
[download]