Do you know what the rodents are? Are they moles? My suspicion is that they are. IF this is the case, moles happen to feed on what's known as Grubs. They're Japanese Bettle larva. It's possible that the crows are poking holes in the sod/lawn too. I live in SE Pa, and around here, early Spring is when we deal with the 'problem' of grubs. There are a few products that you can dump into a spreader to distribute on your lawn. One is called Grub-X. I believe it's made by Ortho.
If it's applied too early, the grubs may be too deep in the soil for the Grub-X to be effective. If it's applied too late, well, your sod may have been already killed either by the crows, moles, or both. Once you have a consistant pattern of non-freezing nights in early Spring, chances are you're OK to apply the Grub-X. The home centers carry the stuff as well as any well-stocked landscape store.
If you have some other type of rodent, post up what it is. If you go to your favorite WEB Search Engine and use keywords like 'grubs' and 'crows' and 'moles', you'll get LOTS of hits on the subject. My best to ya and hope this helps.