Try using an extension usb cable to see if you can get the hdd away from the wii...?This is an interesting problem and I'm glad to see that other people have it, well not glad but more comfortable that I am not alone. Anyways...I started experiencing this type of problem soon after i softmodded and used an external hard drive to run apps. When the external hard drive is plugged in to the usb on the wii I get staticy horizontal lines that scroll up my screen, not too badly but noticeable. When unplugged from the wii usb it is gone. This problem exists even if the wii is off, the interference is visible on the blank tv screen. The problem only exists when I'm using my wii composite video cable, not the regular rca cable.
From reading the other posts on this thread i think it's interesting to note that before i had my wii downstairs in my house where I have a water cooler and every time my water cooler kicked in the screen would blink off and back on again when using my composite video cable. Now i've moved it upstairs and the water cooler problem did not exist but as soon as i connect this usb hard drive i get the other problem I mentioned. I've tried a different outlet and i've wrapped the cable in tinfoil. I will try a few other things and if any success i will let you know but if anyone has a solution for this please let me know.
Since this isn't a common problem there has to be some reason this external hard drive encloser is causing electrical interference through the usb port. I don't know if i need a better usb cable or if the encloser is crappy and emits some noise through the usb. Maybe my only solution is to get a hard drive powerd by the wii so there isn't excess energy interfering.