I would send a nice piece of stationery with wording like: "We're eloping! And we want to celebrate with you! Please join us on (date) at (time) at (location) for a casual backyard party. Food and drinks will be served and we can't wait to see you!" This should be sent about 6-8 weeks out from the date.

You could use any photos you have as a couple, or just nicely decorated stationery. I wouldn't include a RSVP card because that feels too formal. If you need a rough guest count of numbers for catering, I might include, "Please text (name) at (number) to let us know you're coming" at the bottom. But if you're just going for a casual party, I think you could skip that, order plenty of food, then encourage folks to take leftovers like a typical house party.