Yes, you should use a protocol analyzer (sniffer) on the line between your network and your router. And about this traffic... There is nothing strange - somebody may have peer-to-peer software (Kazaa, BitTorrent, eDonkey, etc.). These applications will create steady stream of traffic.
Do you have a firewall between your PCs and your Internet? It could be another point, where you may take a look at the traffic. Firewalls usually create a log when traffic starts, and when it stops. So, you may analyze what happend during the night, when nobody was in the office, and detect who creates this traffic.
Also, if you have access to the router, you can monitor the interface utilization yourself. I would recommend to install MRTG to monitor your links utilization. You can get it as pre-built appliances for VMWare Player. If you don't have access to the router, you may monitor your LAN interface on the firewall.
Good luck,
Mike
CCNP, CCDP, CCVP, CCSP, Security+, MCSE W2K, etc.
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