You need to keep a good amount of free space on the internal drive (the startup volume). 16GB free is too low. Mac OS X uses the free space on the startup volume for hidden system files that are part of its normal operation, including things like virtual memory swap files. Finder copy processing probably also writes hidden temp files into the free space. You should try to keep 10% of the total space free, as a minimum; I use 15% as my minimum, although I've off-loaded most of my personal files to an external FireWire drive, so I have more than 50% free these days.
For your current situation, I would copy some other smaller files (or folders with smaller files) to the 1TB external drive, and erase them off the internal drive. I think the problem is that those .avi files are really large, and that may be a problem with your current lack of free space. So copy over some smaller files first, to get the free space up to about 50GB. Then, try to copy those large files again, starting with any that are on the smaller side. Once you delete them off the internal drive, you will have plenty of free space. You can copy back some of those smaller files you copied over initially (to free up space), if you want to do so, since you should have plenty of free space now.
And remember not to ever get the free space on your startup volume down to 16GB going forward.