The product page (and I guess the manual) for the BDV-E380 lists the following handled media types:
Xvid HD 1080 | YES |
mkv Playback | YES |
MPEG-4 AVC (.mkv, .mp4, .m4v, .m2ts, .mts) | YES |
MP3 | YES (BD, DVD, CD, USB, DLNA) |
AAC (.m4a) | YES (BD, DVD, CD, USB, DLNA) |
WMA9 Standard (.wma) | YES (BD, DVD, CD, USB, DLNA) |
LPCM (.wav) | YES (BD, DVD, CD, USB, DLNA) |
GIF (.gif) | YES (BD, DVD, CD, USB, DLNA) |
PNG (.png) | YES (BD, DVD, CD, USB, DLNA) |
For many of the file formats listed, it's going to be more down to whether the NAS supports them. For instance, my NAS (Buffalo Linkstation Mini) runs Twonky Media Server on it natively, and that cannot support MKV files.
Have a look at the manual (or product page on the web) for your NAS drive to determine what it can deal with.
Cheers,
Dean