Unable to connect to Xbox Live sessions

It's been happening for a while now. There are some people in specific I can't seem to get across to, whether it's joinng parties or playing halo together, and I need an extra person to connect between such people. It says my NAT is open, but I believe the problems coming from me. Maybe it's firewall, my router settings, who knows: I don't know how to operate eithers settings.

Any way to help solve this problem?

You should try plugging your Xbox into the wall without the router and see if it fixes the problem. If it does, then you'll need to mess with your router settings. If it doesn't, then you know it's something wrong with your xbox's settings.

I use a wired connection on a Linksys router. Define "plugginging into the wall without the router" if I intend on this problem not happening online.

I mean take the ethernet that would normally run from the xbox to the router and plug it right into the modem, unplugging the router. Then you're connected to the internet without the modem's interference.

Hmmmm, worth a try.

So how would I know if the xbox's settings have problems?

You would know that it's the xbox's settings that are wrong if when you plug it right into the modem and it still doesn't work.