Oh, the grease stains. Why does party food have to be so greasy? Hot dogs, burgers, frosting, ice cream -- it seems like everything kids eat has to be loaded up with some substance that will resolutely refuse to listen to any soap- and water-based reasoning.
Grease stains are tough, and for the really bad ones, dry cleaning is the only realistic option. However, if you get to grease fast enough, there are a couple of things around the house that can bust up grease before it gets too deep, provided you're dealing with a normal fabric like cotton. Rubbing on some dishwashing detergent as a pretreatment for a grease stain tends to work well, and shampoo, which is full of surfactants that break up body oils, can also do in a pinch. If you're feeling really adventurous (or desperate!), processed cheese from an aerosol can contains chemicals that can lift out grease, too. But then, of course, you have to clean off the cheese.