I think other posters have made good suggestions about using the birthday opportunity as a way giving back to the community in some way. Sounds like your kids might still be too young to FULLY understand, and I would hesitate recommending that you give your kids NO birthday gifts. There's nothing wrong with giving your kids gifts, especially on significant occasions. Though helping them understand and appreciate how to give from THEMSELVES is certainly essential. I like what posters have suggested about asking parents to bring a donation to contribute to a certain cause. Since the kids are so young, getting them involved "helping out" for a half hour or so at a local animal shelter might be your best bet.
I would recommend you stay away from inviting "underprivileged" kids to a birthday party. This will only create awkwardness, both for your own kids and the invited participants - especially if those kids or their parents sense that they are being "pitied" or "given charity" in such a way as to be made into a "lesson" for YOUR kids... That will only make those kids/parents feel self-conscious about their situation and role in society and may do more harm than good.
You could make one aspect of the party be to find some of their old toys that they have outgrown or that they feel they would want another child to be able to enjoy and bring them to a donation center together and explain the importance both of reusing and recycling as well as making contributions to families and kids who can't always afford new goods.
Good luck. Please let us know what happens.