Even if your router is your modem, which is common but still really shitty, you should still have an admin panel within the modem that allows you to setup your devices. Google the brand of the router & modem... usually these telecom companies still use standard manufacturers like Motorola or whoever for their devices.
Google that shit. Login to the Admin backend. Go to your network, look for your devices connected. You should be able to pinpoint relatively quickly which device is what because your computers will have logical names ("FMT-grinder-laptop," etc), and the 360 will probably have some weird ass name. Then, go to wherever you can forward ports or make settings on those devices, chose the X-Box device... 192.0.0.10 or whatever it is, and set that shit up as a DMZ... DEMILITARIZED ZONE. This puts your X-Box outside of the router's built in firewall which usually clears up any connection issues or gafs. You can spend all day trying to guess the right ports to forward for each game, but here's the thing... nobody is trying to hack yuor house or your 360 especially, so just set it & forget it