Generally, asking people to pay for their own meals at a party or gathering is a social no-no, but when times are tough, it can be impossible to cover the costs of all of the attendees of your party. Learning how to tactfully get the message across that you wish the guests to pay for their own food is the best way to say "pay for your own meal" without sounding rude. It can be hard to do, but if you definitely want to celebrate your birthday with a meal, as opposed to something free, learning to correctly word the request is vital.
Send the invitations around four weeks in advance. This is always a good idea when sending party invitations, but if you're asking your guests to pay for the meal, it is important to give them plenty of notice so that they have enough money to pay for the meal.
Arrange a set menu with the restaurant. Getting people to pay their own way at a restaurant is awkward enough, but there is added stress at the end of the meal if you have to work out how much each individual person spent in order to make the costs fair. A good way to get around this is to sort out a set menu with the restaurant you are going to, so you can divide the cost by the number of people who are attending your party. This makes it easier to state on the invitation, because you can simply list the cost rather than saying "pay for yourself."
List the price at the bottom of the invitation. For example, if your meal is going to come to roughly £9 per person, you can write "$15 per person" at the bottom of the invitation. This doesn't come across as badly as saying "pay for yourself," because you are simply stating how much the meal will cost. You may feel as though you are being rude, but your guests are unlikely to expect you to pay for everybody's meal if you can't afford to.
Add an apology if you wish. If you feel rude simply stating the price of the meal, you can write something like, "Unfortunately, because of my financial situation I am unable to pay for everybody's meal. I'm very sorry, and I wish I could afford to pay for everybody. I hope you will be able to join us regardless!" You may be a bit uncomfortable doing this, but the essential point is that you are being honest with your guests. Explain to them why you can't afford it, and they are likely to understand.