To get your stuff over you can use firewire, if you have it on your eMac. You can use a memory stick, an external drive, if your eMac can burn CDs burn your stuff onto a CD. If your eMac is on a network with your iMac share the files with your imac. If you have a server in your house use that. You could email them to your iMac. You could upload your stuff to a free online storage website and download them onto your iMac from your website. If you have an iPod you can use that as a memory stick. (You can also use some MP3/MP4 players).
That's about all I can think of. I think at least one of them should work for you , good luck!