What to do about stray/possible feral cats?

I live in a city in central IL, and have been feeding two stray (feral?) cats this winter - one big orange male that I think I've been seeing around the neighborhood for a few years (unless this is the son of the one I saw a few years ago), and one black female I've seen occasionally for the past year.  I hadn't seen either of them regularly until this winter, but when they started showing up more often, I also put out a box with a blanket, on a wooden pallet - nothing much, but some sort of shelter from the cold.  The black cat has been using it fairly regularly.  I can't get close to either of them, so not sure if they're shy strays or ferals.  They seem to co-exist with no issues...they'll take turns eating at the bowl I put out.  They're not always together, though.

I've caught and adopted two strays in the past - a large male who lost an eye to FIV, and a young orange female - but neither of them were as shy as these two are, so I've never needed a trap before.  I've been putting off making a decision about what to do with them, if anything, but my hand is going to be forced soon, for two reasons:

1. I'm not as worried about the orange male cat, but I think the black female needs to be caught and spayed.  I saw her writhing around the orange male last spring, so she was apparently in heat.  I'm assuming no one else has caught and spayed her in that time.  I saw her twice with a gray younger cat following her this past summer - I'm assuming he was her kitten, though he looked at least 7 months old at the time - but haven't seen that gray cat this winter.

2. The black female recently showed up with a small ragged patch of fur missing on one hindquarter, and a larger ragged patch (about the size of my hand) missing on her other side.  Not sure if that's from a fight, or fleas (I'd think it would be too cold for those), or something else.  I don't think it's ringworm, though it's hard to tell for sure without looking at it from close-up.  While it is going to be warmer for the next few days, I'm concerned about how she'll deal with the cold nights with that missing fur.

I'm trying to figure out what to do about them.  I could buy a trap (the recommended ones seem to be $100+) and try to catch them (or at least the black one)...but that wouldn't happen for at least another week, and then what?  What if she's already pregnant?  And how easy is it to tame a feral cat (if she's feral)?  I'm not sure where I'd do it, because we have two small children now, along with three existing cats, so we no longer have rooms where we could easily leave her in private.  The easier option would be to have the animal welfare people put out a trap and catch her, but they've told me they euthanize ferals, and even if she's not feral, I suspect they would euthanize her in her current state with the missing fur. 

I know this post is sort of rambling...but any thoughts/suggestions?  At this point, I'm planning to call my vet tomorrow to see if he has any advice, but not sure what I'll do after that.

Are there any animal rescue/ TNR groups in your area?  First, google your town/ area and see if there are any places that can help you.  They might lend you a trap, help with the spay/ neuter and vet fees, or they may even come and trap the cats themselves. Maybe call a few vet clinics and see if they have any resources, will lend you a trap, or will give you a discount on the vetting fees.  

Next, you definitely need to trap these cats and have them fixed.  It'll help them be healthier, safer, and will stop bringing unwanted kitties to this world.  You can either release them where you found them and continue feeding them, or if they're friendly, try to get them adopted out.  Another option if they are feral is to contact local farmers and see if they will adopt them as mousers.  Good luck.  Please update here. :] 

Thank you for helping these stray cats. 

The number one best thing you can do for them is to have both of them fixed.  Not just the female.  She is a priority, but the male needs to be fixed too.  Traps can be purchased on Amazon for around $50.  You also can sometimes rent them from Humane Societies.  Doing TNR on them is the kindest thing you can do. 
Socializing feral or stray cats that have feral tendencies can be difficult, but not impossible.  It requires lots of patience.  You need to have a separate room for the cats.  One that is cat proofed too.  If it's a bedroom, the bed should be flat on the floor or picked up off the ground as under the bed is the first place a cat will run to hide.  Large furniture should be blocked off too.  Cats can squeeze into very small spaces.  You do want the cats to have safe places to hide, but not placed where  you cannot reach them. 

If you do trap them, take them right to the vet or spay/neuter clinic.  You do not want to bring them inside first and then have to get them into a carrier later.  You also do not want them to have access to your other pets until they have been given a clean bill of health. 

I can post socialization tips later, but first see about getting them fixed and then decide if you want to try and bring them inside.