I've avoided quite a few deer that have run onto the road, no need to Bo Luke into the sky or even go off the road. Brake HARD, reducing velocity as much as possible, then steer (not yank the wheel like you're a giving a $5 happy ending) around as best as possible. I did glance off a coyote once, and the damage was far less than if I'd hit it square on. Sadly, the coyote still died, but at least my car had very little to be repaired.
No, no absolute right answer as every situation is different, but I do what has worked for me in the past. Keep speeds down in known animal dense areas, look ahead, plan to brake, and be very, very careful in the dark.