Remember that USB is not a RS232 serial port, nor a parallel port. You need a USB driver to interfase Windows with the USB chip in your device. USB devices work at a very high speed compared with legacy ports, so you need a very precise timing subsystem in your (home made?) peripheral.
The solution depends on the specific hardware you used, but most OEM USB interfase chip vendors offer the driver.
What kind of circuitry is in the utility side of your USB device? it can be translated to parallel data or simulate a serial UART just like RS232, but in the end you need at least some data pin and ground reference in order to control devices like a relay.
Also it would help to know what are the output interface voltage levels of your circuit, TTL, Cmos, whatever, and the working voltage of your relay, where you most probably need a current amplifier to drive the coil.
May the 3d force B with U