I just ran # service httpd restart and I'm getting this message:

Starting httpd: [Wed Jan 09 22:05:43 2008] [warn] VirtualHost 127.0.0.1:0 overlaps with VirtualHost 127.0.0.1:0, the first has precedence, perhaps you need a NameVirtualHost directive
[Wed Jan 09 22:05:43 2008] [warn] NameVirtualHost 111.111.111.111:80 has no VirtualHosts
[Wed Jan 09 22:05:43 2008] [warn] NameVirtualHost 111.111.111.111:443 has no VirtualHosts
[Wed Jan 09 22:05:43 2008] [warn] NameVirtualHost 111.111.111.111:80 has no VirtualHosts
[Wed Jan 09 22:05:43 2008] [warn] NameVirtualHost 111.111.111.111:443 has no VirtualHosts
[Wed Jan 09 22:05:43 2008] [warn] NameVirtualHost 111.111.111.111:80 has no VirtualHosts
[Wed Jan 09 22:05:43 2008] [warn] NameVirtualHost 111.111.111.111:443 has no VirtualHosts

Can anyone tell me why I'm getting this error and how I fix it?

A virtual host is running on the same machine, has a different configuration and needs an own name/address/port. If 2 servers have the same name/address/port apache does not know which one of them to take...

so if you need the virtual host give it a different name/address/port. If not just comment it out in httpd.conf ( start the lines with #)
#<VirtualHost.....>
#...
#</VirtualHost>

Here is my httpd-vhosts.conf file:

# The first VirtualHost section is used for all requests that do not
# match a ServerName or ServerAlias in any <VirtualHost> block.
#
<VirtualHost 127.0.0.1 111.111.111.111:80>
ServerAdmin webmaster@localhost
AliasMatch ^/~([^/]+)(/.*)* /home/$1/public_html$2
DocumentRoot /var/www/html
ServerName localhost
ScriptAlias /cgi-bin/ /var/www/cgi-bin/
CustomLog /var/log/httpd/homedir.log homedir
</VirtualHost>

<VirtualHost 127.0.0.1 111.111.111.111:443>
ServerAdmin webmaster@localhost
AliasMatch ^/~([^/]+)(/.*)* "/home/$1/public_html$2"
DocumentRoot /var/www/html
ServerName localhost
ScriptAlias /cgi-bin/ /var/www/cgi-bin/
CustomLog /var/log/httpd/homedir.log homedir

SSLEngine on
SSLCertificateFile /etc/httpd/conf/ssl.crt/server.crt
SSLCertificateKeyFile /etc/httpd/conf/ssl.key/server.key
</VirtualHost>

My understanding is that I need both of those don't I??

Have you tried something like this instead?
Alternatively, instead of <VirtualHost 127.0.0.1 111.111.111.111:80>, try <VirtualHost 127.0.0.1:80 111.111.111.111:80> and instead of <VirtualHost 127.0.0.1 111.111.111.111:443>, try <VirtualHost 127.0.0.1:443 111.111.111.111:443>