There are many reasons you could have high traffic volumes at night. Besides malware or filesharing many companies are moving to cloud based backup systems, and set up their backups to be at night. The first thing I'd do is contact heads of server groups and inform them of the problem. Ask them if they have any jobs going, and tell them it is impacting services. If your network supports QoS, look to get it set up to guarantee bandwidth to vital services.
If the traffic does not seem legitimate, or you are not getting any help from your internal groups, then you need more information. Most network devices with any intelligence at all can give you port statistics, and most can be polled with snmp. Talk to your network people and see if they have cacti, solarwinds, or the like. If not, set up cacti or another free snmp grapher and start collecting information. Once you have a few days of stats you can then see which ports are using the bandwidth, and you can find what's attached to the port. Look up the MAC address of the device and then map it to an ARP entry, then do a DNS on the IP from the arp table.
Once you know the offending machine, you can then investigate the cause. Find the owner of the box and tell them it's causing trouble, get them to investigate it. If you are the owner do your own investigation. Look for legitimate causes first, there are plenty of them. Once you exhaust those look for malware, you may need to do a span of the port to see what traffic is being sent.