Q: Can't Sync Video

See:

iTunes: May be unable to transfer videos to iPhone, iPad, or iPod

iTunes: Frequently asked questions about viewing and syncing videos

The 2G supports:

H.264 video, up to 1.5 Mbps, 640 by 480 pixels, 30 frames per second, Low-Complexity version of the H.264 Baseline Profile with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats;

H.264 video, up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Baseline Profile up to Level 3.0 with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats;

MPEG-4 video, up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats

.mkv format is not compatible with the iPod. You have to convert the format ro one compatible with the iPod. In my first reply I provided the formats that the 2G iPod supports.