For EyeTV USB:
The MPEG-1 streams that EyeTV produces have the audio and video intermixed, or muxed. Due to a limitation of QuickTime they cannot be directly edited.
There is a long and involved process to convert the MPEG-1 streams that EyeTV produces into something that iMovie can edit. You have to separate the audio and video streams, convert them into a different form, and then recombine them.
You'll need these programs:
SoundApp
(a free audio conversion program which works in Classic or OS 9)
http://www.spies.com/~franke/SoundApp/#download
bbDEMUX
(a free MPEG demuxer which is for OS X)
http://prdownloads.sourceforge.net/macbbdemux/
MAD
(a free audio conversion tool for OS X)
http://www.biermann.org/philipp/mad/
Do the following if you want to edit in iMovie:
Export a recorded program from EyeTV, by using the File --> Save as QuickTime command.
Demux the file that EyeTV produces. You'll get a video file which ends with .m1v, and an audio file that ends with .m1a
Use SoundApp to File --> Convert the .m1a file into AIFF format. You can also use MAD to convert to AIFF if you want to stay in OS X.
Use iMovie to import the AIFF file - it shows up as an audio track at the bottom of the screen
Then, use the QuickTime Player to File --> Export the .m1v file to DV.
Please note that the DV file size that iMovie accepts is limited to 2GB (9 minutes or less). Trim your video file into smaller segments before trying to import it.
Use iMovie to import the DV file - it shows up as a video clip on the top right of the screen
Drag the video clip to the bottom of the screen, and now the video is synched back up with the audio.
Edit the recombined movie to your specifications.
After editing, you can export your movie in QuickTime format, or keep it in DV for use in programs like iDVD.