When you have a lot of paper money together, it's called a wad (bundle). If you are "wadded up", it means that you have a good deal of money (relative to your situation). In this case, the speaker has enough money that he/she feels it possible to pay for everybody without trouble.

That expression means that you have enough money and will pay for your food and for the food of those you invited. If you say you have a wad of cash it means that you have a handful of banknotes in your pocket. This saying pre-dates our electronic banking system and comes from a time when a handful of dollar bills were still worth something. In those days the recently rich also showed off by carrying wads of money in their wallets.

He's got wads of notes (money).

A comparatively large stock or quantity of something, especially money: He's got a healthy wad salted away. To roll tightly (often followed by up): He wadded up his cap and stuck it into his pocket. To form (material) into a wad. To fill out with or as if with wadding; stuff; pad: to wad a quilt; to wad a speech with useless information.