What genre is this soundtrack from Commedia Sexy?
I would say jazz swing but it's a too broad description to find any similar tracks.
Can you name similar tracks, especially in this style you can hear from 1:00 on, with bending "screaming" clarinet and jazz orchestra?
It's a sort of pseudo 1930's type swing. Some of it sounds similar to recordings that Benny Goodman made around that time. If you like this, you should listen to any of his recordings (nearly all of them are good) either with his orchestra or his quartet. You might also like Artie Shaw or maybe the Duke Ellington Orchestra. Try starting with Benny Goodman's "Sing, Sing, Sing".
The song is a pastiche of early jazz styles, and is perhaps most influenced by the pre-swing early jazz sound called "Dixieland" or "Hot Jazz." Originating in the African-American dance bands of New Orleans, the style is anchored by a fast steady rhythm line (which in your sample is taken by the repetitive chords on the piano, but which would have originally been a banjo) with melodic improvised solos on top by a variety of instruments (the clarinet in your sample).
The minor key pushes it in the direction of what is often known as "gypsy jazz" or "gypsy swing" after the great Roma guitarist Django Reinhardt. (It's worth noting that many people now consider the term "gypsy" to be a racial slur! For that reason, you might prefer to use the alternate genre name, "hot club swing," after the "Hot Club" of Paris). Hot-club uses a guitar as the rhythm instrument, however, so if you're primarily interested in the piano/clarinet sound, that might not be the best reference. (There are, however, hot-club style recordings that do feature clarinet.)
In terms of other similar songs, this has (probably deliberate) echoes of the iconic 1930s Irving Berlin hit Puttin' on the Ritz, and the "Christopher Columbus" section of the Benny Goodman version of Sing, Sing, Sing.
