The HAI wireless vehicle sensor works really well. I have one at the end of my 500' driveway buried in an irrigation valve box and it still detects vehicles as small as my riding lawn mower. It runs for years on 2 C batteries.
The only costs there are the sensor itself, ~$150 and the receiver, ~$70.
Then the wireless receiver can be used for other things if you need(so its cost is amortized the more zones you hook to it), like key fobs and other zones.
As for the tie in. A couple ways I can think of.
One, you can use the wireless receiver I referenced above and a keyfob as the garage door opener.
You hook the Omni to the door opener to control it through one of the Omni outputs and a dry contact relay and discard the RF remote that came with the door.
When you press the keyfob button, the Omni sees the button, bypasses the zone for a set period of time and then the Omni sends the open command to the door.
You can bypass the door or doors for a set period, say 10 minutes, or disarm the system completely if you prefer, but that means if someone gets a hold of the keyfob they can disarm the system.
The second way would be to get a retrofit garage door RF receiver. These are used to add RF capability to older openers or to upgrade to more secure rolling code technology.
Something like this:
http://www.ecrater.com/p/2189134/genie-36163r-model-315390r2-dual
So a button press on the garage door opener would be simultaneously received by the door opener and the standalone RF receiver.
The RF receiver would be hooked in to one of the Omni zones to signal the Omni of a valid opener code, and then bypass the zone for a set period.
The trouble with this method is it is possible the door starts moving, and thus is detected as "NOT READY" before the Omni processes the bypass, so the alarm would be tripped.
You could use this method to disarm the system, but the same danger exists of someone gettin a hold of the remote.
You could also use this method similar to the method above and use the RF remote and receiver in place of the HAI wireless receiver and keyfob. Wipe the codes form the actual door opener and have the Omni open and close the door when the stand alone RF receiver after it bypasses the zone.
That last method is probably initially less expensive than using the HAI receiver and fob, but you lose any future expandability.