Ok first off DNS does not redirect to folders or ports. It maps a fully qualified domain name (www.example.com) where www is the host and example.com is the domain to an IP. Now you can use cnames to point www.example.com to host.otherdomain.tld for example.. But that is it..
if you have http://host.domain.tld and you want to direct it to http://otherhost.oth...n.tld/something that is NOT done with dns, never was, never could be. Now its possible dns providers provide that service - but its NOT done via dns - they listen for traffic at where host.domain.tld points and then send it where you want to go with a http redirect, etc.
You can have yourhost.yorudomain.tld that is registered with godaddy point to whatever IP you want that is reachable via the public net 10.x.x.x is private rfc1918 address space and is not useable on the internet - I can not tell if you are just using that as an example or if that is what you want. If you want to use IPs for examples rfc5737 lists The blocks 192.0.2.0/24, 198.51.100.0/24 and 203.0.113.0/24 for use in documentation.
As to running multiple servers? You can provide as many sites as your http server can handle with just 1 instance in multiple ways.. You can have your server listen on multiple IPs that is assigned to the server, you can use different ports ie http://yourhost.yourdomain.tld:8080 you host headers or virtual domains where the http server knows that host.domain.tld gets served up from /folder1 on the server and host.ogtherdomain.tld gets served up from /folder2 or otherhost.domain.tld gets served up from /folder3
You can also use host.domain.tld/site1 host.domain.tld/site2 as ways to access sites off different web servers but you can direct to those with DNS.
If what you have is 3 different domains with godaddy, lets call them domain1.tld and domain2.tld and domain3.tld and you want people on the internet to go to your home public IP, then in dns point to your IP, or use dynamic dns service to auto change this IP if your isp connection changes, etc.. So
www.doman1.tld points to publicIP
www.domain2.tld points to publicIP
www.domain3.tld points to publicIP
Now on your router forward 80 to your webserver privateIP. On your webserver be it what tomcat, then here is instructions on how to do virtual hosting on tomcat
Google for tomcat virtual hosting - there are many guides and howto's