There are some good responses below already.
You have a colony, is what it's called.
You're right to worry, they won't wander successfully if it's a highly wooded area. While overwhelming at first, and if it's any consolation, I have about that much and it's not a huge deal to feed them dry food. I feed mine wet twice a day and they are spoiled so that's a WHOLE other thing.
Couple bowls of food during the day, take it in at night so it doesn't draw wild critters. Keep water available at all times. Big bowls nearish the garden hose will do. That's kinda it once the spay/neuter is done. If any have a corner tip of a left ear cut off, they are already spay/neutered for sure.
Honestly, picking up the litter from the boxes is the most work with that number of cats plus entertaining them. Your cats have woods, yay! And the previous owner was probably right - they will pick off the rodents and I'll bet they are definitely around. Yuck.
As you know already, your best bet is to get them neutered/spayed, try to adopt out any who are domestic - get any domestic you don't fall in love with to a rescue, not a shelter b/c they will most likely need resocializing )(maybe) and aspca shelters or animal control don't have time for that.
That way you control the number and they don't multiply. Multiplying is the big problem, and that's easy to stop. The kittens your preggers cats might have can be socialized, fostered and adopted out through a rescue - who would be good at weeding out creepy people.
I'm not sure where you are located but if you are having trouble finding affordable TNR solutions or local rescue mentor, I can pass your info onto a rescue mailing list I'm on. If you are interested, please PM Me.
If you are lucky, you can get a rescue to sponsor at least some of the spay/neuters and maybe to help cover the cost of medical for the ones which are sick. You can also try to www.gofund.me to raise funds or some other fundraising site. That will at least help, and I'd be happy to pass that on too.
What I'd try, along with some great suggestions below:
Reach out to a local rescue or google low cost spay/neuter or google your town's name + Trap Neuter Release and some rescues or your local humane/spca will pop up. Ask them if they can recommend where to go for low cost TNR or a rescue to talk to about this. Ask if anyone nearby is having a free spay/neuter day and that should get you a start on some good info.
There might even be a mobile spay/neuter unit in the area - those do exist. You can also look for a vet who comes out to farms and see if they have any spay/neuter contacts, if they don't do that themselves.
Look around for a vet school if they are volunteering anywhere for a TNR event.
Another local feral colony caretaker might show you a few tricks to keep your costs down in terms of medicine, flea medication and upper respitory stuff, those are the most common issues and can be resolved on your own a lot. Ask around at the pet stores/feed stores - find a local buddy.
http://www.neighborhoodcats.org/ might also be a good resource and has good list of winter shelters should that be a thing. I'm kind of assuming they have a shelter somewhere already.
Sorry you got left with the furbabes like that and so glad you're looking for help and a way to sort it out responsibly. Good luck, and reach out if you need, like I said.