How can I get rid of very large hornets living under the cedar shingles of my house
Were you able to find the nest? That would be the key piece of info before you can start planning your attack. There are all sorts of pesticides that can be sprayed, including foaming ones that may help here since they expand and may help sealing the area. Be sure to either work at night or be very quick (or wait until winter, which may take care of the issue on its own). Also does not hurt to find out if you have any unusually strong allergies to wasp's poison before you engage in the extermination. If there's a risk on allergy reaction, paying $200-300 to a professional exterminator may be a much better option.
One other thing: which exact species are they? If they are paper wasps, you might seriously consider just waiting until winter since they don't return to their nests, are not aggressive and useful for the garden - they eat the bugs you decidedly do not want on your plants. So, anyway, there's a couple ways to approach this, including not approaching at all.