It was well known that Blake Edwards was an enormous Laurel and Hardy fan. You can see it in the Pink Panther films. And no where in his work is that more evident than in The Party. The L & H influences and touches are everywhere. The running gag of the drunken waiter who speaks only one or two words in the entire film. The careful building of gag upon gag, each one funnier than the one before it. The reaction shots that top all the gags. The comedy of embarrassment. (Babe Hardy would be proud!) There are some funny lines for sure but the biggest laughs come from moments that feature no dialog at all. There is very little slapstick until the end. But the humor is visual and based on character just as the best stuff in Laurel and Hardy was. In my opinion the boys invented situation comedy. Television comedy owes a big debt to Laurel and Hardy. They probably don't even know it.
