One of my friends is having a birthday party for herself at her house. She has invited people but asked everyone to bring a dish and given out a list of things they need for people to tick off. This encompasses everything you might have at a buffet plus alcoholic/non alcoholic drinks to I assume that this means she is not providing anything!
There is nothing saying that we are not to bring gifts either so she is clearly expecting pressies too.
Said friend and her husband are fairly well off so well able to afford to cater for the small group that have been invited.
I understand that if someone is having a general get-together like a BBQ and offering their house as the venue you might ask people to bring a dish but if you are actually having the party to celebrate your own birthday surely it is quite rude to basically ask people to pay for your party!