Does your router have the ability to show IP's connected? Any of those showing a lot of strange activity?
TCPdump may show what's going through the connection. You could route traffic from your router to a virtual machine and forward it from there so you could sniff intercepted traffic and see what's going through the connection.
Anything unusual in the logs on any machines?
What about network interface statistics on your machines? Reset statistics and see what's going on there.
If your machines are disconnected for a period of time from the network, is your router still showing high levels of activity?
Does your router show connected workstations to it, or can you sniff for MAC addresses and/or rogue IP's on your network if you have wireless?
Did you run virus/malware scans on all your machines, keeping in mind that they can only tell you whether you ARE infected, not that you aren't (in other words, it's not 100% reliable since malware can cloak itself if it's clever)?
The best thing to try doing in my opinion is get another machine in the network to sniff network traffic and look for anomalies. If I'm reading your traffic stats correctly you're getting a huge amount of incoming traffic, not much outgoing, so either someone is downloading a lot of stuff or you're being hit with some kind of probe or attack. If you can't narrow it down in your network contact your ISP and see if they can see what's coming into your connection from their side; they should be able to determine a little better if you're under a denial of service attack. Check your router, check with packet sniffers, check using a clean VM and redirect all traffic with ARP poisoning to see if you can detect where the activity is coming from.
If you have wireless, try shutting that off to determine if there's another person on your network (if you don't have a router/AP that tells you the MAC of attached workstations already).