To read the data via a USB enclosure you can try one of the tools listed here:
http://www.howtoforge.com/access-linux-partitions-from-windows
I did not try any of these myself, but if I hook up the drive to a Linux machine it can read the data w/o any problem. The partitions are typically formatted ext2 (older firmware) or ext3 (option in newer firmwares). (There is a small partition created on each drives, where config data is stored, do not touch those. Look for the big data partition.)
I am pretty sure there are tools to do this on a Mac too, although what I found is not that promising:
http://discussions.apple.com/message.jspa?messageID=9433712
If you are using two drives in RAID1 (mirror) mode I would advise against writing anything on them outside of the DNS-321, that would seriously mess up the raid. Theoretically you could re-sync after, but there are many posts complaining about re-sync problems, so I would advise against it. (If you are not using raid you can write data using the same tools that let you read it.)
If your laptop has no Gb network or you have no Gb switch, you will have to wait. And wait. Try to do 20GB at a time. Even over Gb the speed will vary depending on the file sizes. Writing lots of small files should be slower than fewer but bigger files. I have a Gb network and recently uploaded about 100GB data of large files - that took about 3.5hrs. Moving 400Gb over a 100Mbs network... will take time. Sorry.
Actually once you confirmed that you can read the data, you can just put the two new drives into the DNS-321, format, setup raid1, hook up one of the old drives (I assume you were using mirroring, so they have the same data) via USB to your laptop, mount the DNS-321 and start copying the data from the old drive using the laptop via the network to the DNS-321 with the new drives in it. This won't make your network speed any better, but at least you don't have to copy the data twice....
Post your experience. Please.