You don't need a router, I think at least the eMac and depending on your iMac they should be auto switching network interfaces. Which means you can plug an ethernet cable directly from one to the other. No router, and no cross-over cable. And this is made especially easy because the two macs will see each other. And its even better with apple talk enabled.
I've done this, it's easy.
Oh, bother, where is my brain. You can also just use FireWire. And use drive mode on the eMac, it will act like an external drive.