Ah, good old foley - the mystic art of inventing sounds to use in creative ways. The practice originated with the old radio serials which were broadcast live, without the benefit of any sort of pre-recording or editing. Around the same time, it was also used to accompany silent films - foley artists would watch the film from behind the screen for cues when to contribute what sound.
Trivia Time: The practice was named for Jack Donovan Foley, who began his career with Universal Studios in 1914. For more than half a century (until his death in 1967), he was THE go-to guy for sound effects in all mediums. Simply called "our Foley" or "Foley artist" at other studios, the position was officially renamed "Foley" in his honor.
Tregoweth Brown of Warner Brothers is credited with introducing the sound in 1931. Dissatisfied with most foley efforts and having access to EVERY sound effect in the studio's library, he commandeered a long panic stop from The Public Enemy, found a fraction of the effect he found particularly appealing, and repeated it several times in rapid succession.
The rest, as they say, was history.
The running-in-place bongo sound was, indeed, created by using bongos.
The classic "psheeeewww!" sound mentioned was typically created by whipping a thin reed past the microphone very quickly.
Most bone-related injuries (including a smashed head) were created using frozen romaine lettuce.
"Bonk"s and "clank"s are far too varied to make a comprehensive list - ranging from bicycle horns to clapping a metal trash can with a wooden spoon to large gongs.
More Trivia Time: For those who don't already know, the famous sound of the TARDIS from Doctor Who (which has remained in use for more than half a century) was created when Brian Hodgson, studio manager of the BBC's Radiophonic Workshop, dragged his house key along one of the strings of the studio's broken piano (which was awaiting repair).