Keep in mind if you're dealing with gas around chickens that bird lungs are especially sensitive to toxic gas and things like smoke even in open air situations. You'd have to have them all cleared out of the coop and far away. You would not want to use your car, canister CO2 would be best, this way you can control how quickly the levels in their home is rising. If it is kept far too low too long (like with dry ice) or introduced too high with other irritants (like with car exhaust) they are going to be in a lot of pain, panic, and do their best to flee. Good CO2 control leads to them passing out before they feel the urge to escape. It is all very testy, and it leaves all those bodies in the concrete. Wish we had access to expanding CO2 foam like they use to mass euthanize large groups of animals in cases of disease outbreak but it asphyxiates so quickly I can see why it isn't widely available...
I would think if you have lots of rats to deal with in a small amount of time, electric box traps or large drown traps would work best. Drown traps are cheaper, but sadly less humane. You can also use a game camera to see where the entries and exits are during their prime night time hours for good trap placement.
This might make me unpopular but... it wouldn't hurt to invite some bigger snakes to your property! The most helpful colubrids are tunnel hunters, they won't be able to eat mom and dad in most cases, but they'll crush the entire litter against the wall of the tunnel and eat them all in one go. Way more effective than cats, and not damaging to the environment. Snakes are your friends! If the rat's traffic is where you feel comfortable doing so maybe make a brush/tin pile to try and invite one in! Just be educated on your local venomous and be reasonable if you happen to see one, you're not going to be hurt by 'em if you don't get in their face, and if they do decide to make a home there you can always take away their brush pile.
Edited by Skink - 5/8/16 at 10:19pm