Tables and seating are the two main challenges to entertaining in a small space. Dinner parties are really just cocktail parties if you don't have a central dinning area where everyone gathers to talk, drink and tell great stories. Most people in studios don't have the space for a large dining table, but there are many fun alternatives to eating at a traditional dining table. You can take advantage of what furniture you already own and push your dresser, desk and other tables together to make one large surface. Don't worry if your dresser is a little bit lower than your desk. You can either leave it uneven for a cool "thrown together" look or you can prop up your furniture with sturdy books, for a smooth dining surface.
Another idea is to find some large sturdy boxes and build your own temporary dining table. Just stack them together into whatever modular shape you want and use your trusty roll of duct tape to secure the boxes together into one solid unit. Since boxes wrapped in duct tape might not be the most pleasing aesthetic for you guests, buy or make a tablecloth to put over your makeshift dining table. If you don't own a large tablecloth, you can buy a cheap flat sheet from any home goods store. Then you can customize it for a pulled together look.
Having enough chairs can also be a problem in a small space, and I wouldn't suggest using cardboard boxes as an alternative. Sturdy boxes might work as a temporary table, but they may not be safe for sitting unless you want your friends randomly crashing to the floor throughout the night. Just look around your apartment and find furniture that can safely hold the weight of a normal person. Friends can sit on your coffee table, side table, even part of your bed, if you provide a nice little cushion. Also, if you are friends with your neighbors, don't be afraid to ask if you can borrow a few chairs for a night. They probably won't mind lending out some seating and might reciprocate the next time they have a party!