First, just to make sure, you do have an exemption from the IRS as a 501(c)(3) organization, right? Because if you do not, nothing anyone gives to you is deductible as a charitable contribution.
If you take in cash from people, what are you doing with it? Are you depositing it in the PTO bank account, or are you depositing it in some kind of special trust account that is not in the PTOs name, or what?
Keep cash donations out of your PTO bank account!
If you are putting it in your PTO account, it is going to count as PTO revenues and you are going to need to put it on the PTO tax return. Also, if people are stipulating that this is cash to help with disaster recovery, you need to make very sure that your financial records are kept in such a way so that you can prove that that is exactly what is was spent on. And yes, you would give people a tax deductible receipt for that--they have made a donation to a qualified charity.
It does get a little tricky, though, because then how you spend the cash probably does not necessarily fall into your typical mission statement. Technically, the IRS could call you on that and create some problems (that's the type of thing they would yank an exemption for). However, let's face it, the likelihood of that is pretty darn slim--and even if they were to catch it, it's clearly a one time thing with extenuating circumstances, so they'd be foolish to do anything. But, nonetheless, I don't think it's something you should be doing. Dealing with cash donations for something like this is best left to professionals in that area. If the intention is to funnel cash to the kids that have relocated to your school, a better bet is to work with a bank there to set up some kind of trust fund that the money would go into. I believe donations to those types of funds are generally non-deductible, but I'm not sure.
If you take in non-cash items, it sounds like they're probably non-deductible. If people are giving clothes, etc., to specific identified people in your school only, that's sort of like an "adopt a family" program. In that case, those are just gifts to those families, and are not deductible.
All that said, while I'm an accountant, I'm not a tax accountant, so the advice is probably worth about as much as you're paying for it....