Ahoy there!
I have been having almost exactly the same issues as you (Well, not exactly, as I freeload my games, but still) - The main problem you're having is that Xbox360 (and almost all games these days, especially on Wii,PS3,Xbox360) display normally at 60Hz - this the frequency which most consoles project at (and anything from US or Japan broadcasts at this frequency).
I'm not sure why, but alot (almost all) of USB capture devices, unless they specifically say DC60+, or unless they support what is called NTSC 4.33, you will not be able to record your games in 60hz.
Please see
http://forum.easycap.co.uk/index.php?topic=42.0 or my ongoing thread
http://forum.easycap.co.uk/index.php?topic=43.0 or
http://forum.easycap.co.uk/index.php?topic=24.0All three links above suggest this, and the only way you can get your Easycap to display in this (if it doesn't support the NTSC 4.33/60Hz modem) is to change your Xbox's display settings to 50Hz. I have a huge amount of issues getting this working, and though I have yet to receive my DC60+ easycap yet, I have faith that I have this issue sorted. Most cheaper easycaps (especially the Easycap 108, which I and many others have...because it's cheap) have this issue.
Please also see
http://forum.videohelp.com/topic361694.html - which has more info
The actual item you need is something like this
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&ssPageName=STRK:MEWAX:IT&item=110340801969Or
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&ssPageName=STRK:MEWAX:IT&item=110340804430I do hope it helps! If you have any other questions, feel free to ask.
Kind Regards,
Fenberry