MRTG should work just fine with private IP addresses.
1) Make sure the target of your MRTG query isn't running firewall software that prevents SNMP requests from your MRTG server.
2) Make sure you aren't running TCP wrappers (a hosts.allow file that isn't blank) that prevents SNMP queries from the MRTG server.
3) Make sure the routing on the target device is correct so that your MRTG server can correctly access it. Try using "ping" or try to log into the target device from the MRTG server as a test for this.
I see where your ISP has given you an RFC1918 IP address. This is invalid on the Internet and they are probably doing NAT to a real Internet IP address somewhere on their network to provide you with Internet access.
An SNMP query to this RFC1918 IP address from the Internet will fail. You may need to ask your ISP for a non private space IP address, or get them to set up a 1 to 1 NAT for you to allow the query.
I don't recommend doing or allowing SNMP queries over the Internet. SNMP is un encrypted and you run the risk of sensitive data such as passwords, bandwidth data etc being intercepted by unwanted eyes.