We are a non for profit 501c organization. We are planning on flying approx 45 kids to Ireland.
Do we have to pay the tax on airfare?
Do we have to pay the VAT (Value added tax) in Ireland for hotels?

Ask the airline if your 501(c) status exempts you from the tax; probably not.

You will have to ask the Irish tax authorities on the hotel to be sure, but probably yes.

I agree with ATE. In general your 501c(3) status exempts you from paying income tax, and may be used to exempt you from paying sales tax in certain curcumstances (depending on on the rules in your state), and religious and educational instituitions are exempt from local property taxes, but that's about it. You still pay excise taxes on your phone and cable lines, gasoline taxes at the pump, liquor taxes if you buy a bottle of wine, payroll taxes on your employees, etc. The point is that the 501c(3) status does not exempt you from all taxes.