I'm sorry to hear that the church has let you down as an institution rather than as the body of Christ it should be. Have you tried personally approaching the deacons of a particular church (the deacons are the people directly responsible for assisting the needy of the congregation and the community, as they were in Jesus's day responsible for 'widows and orphans'...) and spelling out exactly what your needs are? A grocery store voucher to get food for Christmas dinner, a Toys-R-Us gift card for the kids, a gas coupon or transit card?
You don't say how old your children are, but if they are old enough to expect gifts, they are old enough to have you sit lovingly with them and explain that 'we' (as a family) don't have enough money to buy a lot of presents this year. If you are so short that you are doing without food yourself, toys should not really be a priority. Consider this: if you fall ill, who will take care of your children? Adjust your own oxygen mask first, as they say on the airline safety drill...
Having said that, there are plenty of thrift stores and dollar stores where a few bucks can go a long way for some presents.
Try checking out the wonderful links online (because obviously you have internet access) such as http://www.suite101.com/article.cfm/being_thrifty/86076 - or Google yourself for phrases such as 'budget christmas' or 'thrifty christmas'. Pioneers managed to keep the Christmas spirit alive without store-bought decorations and gifts; showing the love you have for your boys is the best thing you can do.
Keep your courage and your faith alive, and make sure you take care of yourself as well.
Love,
bardmistress