How do I use subfolders of my server's IP address as their own "domains" without a FQDN

You can use IP addresses in virtual hosts too, e.g.:

<VirtualHost *:80>
  ServerName 1.2.3.4
</VirtualHost>

For the userdir module:

sudo a2enmod userdir
sudo service apache2 restart

Apache uses the users on your droplet, so to add others:

sudo adduser newuser

… which creates the directory /home/newuser

sudo mkdir /home/newuser/public_html
sudo chmod 0755 /home/newuser/public_html

Apache will now serve files out of /home/newuser/public_html at the address http://1.2.3.4/~newuser.