Yes it's illegal to kill Canada geese in Virginia and any other state.
Canada geese are a federally protected species under the Migratory Bird Treaty Act and you could face prison time and or fines for killing a Canada goose.
That is unless you have a permit to kill the goose that is causing issues but you would have to get the permit and have a very good reason to legally kill the Canada Goose.
If you do need to repel Canada Geese you can use humane repellency methods such as dogs, lasers or other frightening techniques to get rid of the Canada Geese.
As for other geese you might be able to legally kill the geese during hunting season but usually not before then.
If you do hunt other geese in Virginia you require A HIP registration number, a federal migratory duck stamp, and a Virginia Migratory Waterfowl Conservation Stamp (unless license exempt) to hunt geese during the hunting season.
According to Virginia law Electronic calls and unplugged shotguns are not allowed for hunting Canada geese.