Consult with the local rat exterminators. They know the most about it. Rats can get in via VERY small openings. Is your under-house zone open enough that CATS can get under there? If not, you might benefit by making it so. Our chicken house had a big problem because rats fit under it but cats did not!

We had a really good Orkin guy in Richmond VA named Lorenzo. He gave my wife and I copper wool to stuff around entrances into the home. Rats can and will chew through just about anything but the copper hurts their teeth. He used copper because steel wool has finer threads and when it rusts, becomes very brittle. The copper strands are flat and wide in comparison.

I've had to deal with this in the tropics in the agriculture industry, particularly in small packhouses in very rural areas. Our approach has always been inspect, seal everything possible, and put out poison bait stations as a last resort, preferably in some type of enclosures that limits entry by other animals. Your deck situation sounds tricky. Have you thought of a cement footer around the perimeter of the deck to which you anchor some type of barrier, such as wire mesh or similar?

I've heard of the steel/copper wool solution, but it means having access to entrances to seal them. In which case you may want to make part of the deck flooring removable, like trap doors, to better access the area.