I think you're going to have to ask Softlayer directly, or try them out ,but you can rule out iSCSI SAN, not because of performance, but because you're looking at a shared filesystem to maximise utilisation, rather than raw block access for performance.
NAS will be easy to use, mount a shared filesystem on each boxes, and just copy the files to that filesystem.
Evault I've not got a clue about but it looks like it's Softlayers brand for snapshot backups of servers, so it does a full copy of the server without downtime. It sounds like it does de-duplication of data, which could generate significant space savings (and so cost-savings) for you.
Cloud storage is generally a term for storage accessed using web protocols like webdav rather than NFS or CIFS for NAS storage, you'll possibly have to run dedicated scripts to copy files to and from it depending how Softlayer have it running.
In terms of performance, each one of these options could run just as fast as any of the others depending how Softlayer actually have it configured and the hardware behind it, but the Evault system sounds like it's their own preferred option for your requirements.