There are many styles of laughing songs from the 20's onward. Besides the contextually anachronistic Strauss, other pieces titled The Laughing Song incorporated laughter into their melodic structures, such as those by Maurice Farkoa and George W. Johnson. However, the ones that adhere to the following formula are hands-down my favorite kind of laughing songs.
The formula is simple: A musician (usually a trumpet or trombone, sometimes a voice) starts a piece of music. They're interrupted by someone else's laughter, but attempt to keep going. The laughter becomes contagious and eventually takes over. The end. These records were big sellers in the 20's, with the Okeh Laughing Song being the most well known.
It sounds a bit predictable, but is it really much more so than typical song form, which Van Dyke Parks described as "the most portable piece of cultural baggage we can carry?"
Here are some great laughing records that I found online, in chronological order:
The Cameo Laughing Record (1922):
Sally Stembler and Edward Meeker's Laughing Record (1923):
Paramount/Puritan Laughing Record, and the Spoiled Cornet (both 1923):
Melotone Laughing Record No. 2 (1936)
Spike Jones' Laughing Record (1940's?):
Finally, the Okeh Laughing Song as used by Tex Avery in SH-H-H-H-H-H:
I know there are more out there. If you know of one that follows this format, please do send it my way!