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]