I think its an oboe.... you know what I'm talking about.
What you are calling "Jewish music" is probably a specific style called Klezmer. Klezmer music is a product of the Ashkenazazi (Yiddish-speaking) Jewish people of Central and Eastern Europe. The word klezemr is probably derived from an late medival hebrew coinage meaning "musical instrument", as כְּלִי זֶמֶר literally means "vessel of song".
The word klezmer is first attested Yiddish sources in the later 15th century, where it refers not to a style of music but to the "klezmorim" whom were apparently a type of itinerant musican.
However, the modern style of kelzer music and most of the familiar melodies are the product of the mid-19th century, mostly from the region area around what is today eastern Romania and southwest Ukraine -- historical Bessarabia and it's surroundings.
Klezmer music was mostly dance music, performed by groups of itinerant musicians, not always Jewish themselves, whom traveled from town to town, village to village, and made their living hiring themselves out to play music for weddings and other such festive occasions. It was this background that gave the original klezmer it distinctive selection of instruments. Instruments that were portable and could easily be played while standing or held from a shoulder strap, like the violin and flute (and later the accordion), were favored. The oboe later became common because it's sound mimiced a traditional wooden flute, but the oboe has a wider range of keys and notes it can play. Smaller drums might also be used, but the larger drum kits and even pianos sometimes seen in contemporary klezmer music are a development of the mid-20th century.
Klezmer was, in origin the dance-hall or party music of the Jews of Eastern Europe, but it was never an exclusively Jewish pursuit by any means. The traveling Jewish folk musicians of 19th century Eastern Europe worked as both clients and collaborators with other peoples living the region, including Roma, Ukrainians, and Hungarians. Elements of their folk music traditions made it's way into klezmer, but a description of the exact musical terminology is beyond my abilities, I'm sorry to say (see the source list for further reading on this matter).
I want to emphasize that rather than being a distinct style, until the early to mid 20th century, klezmer was defined by whom played it and in what venues, not by it's musical qualities as we understand and evaulate it today. In the vernacular Yiddish literature of the 19th (and early 20th) century, klezmer was music made by klezmorim, the traveling musicians. Most of the academic research on the original Eastern European klemirim was undertaken in the 1920s and 1930s by Soviet Jewish folklorists and ethnomusicologists whom were trying to build a narrative about the existince of a "secular Yiddish proletarian tradition", and idea with only a limited basis in observable reality. Nevertheless, current scholarly literature owes a great debt to these scholars, epescially people Moshe Beregovsky.
Side note: Moshe Beregovsky is also infamous as one of those scholars whom wasn't too picky about how his name was transliterated into Latin characters, so if you try to find his work in a modern American library, I've found as many as five or six different variant spellings: Moisi Bergovski, Moses Bergovskii, etc.
The oldest documentation of the practices of the kelzmorim in the 19th and early 20th century comes from these ethnographers, whom were in a position to interview elderly perfomers whom had been trained in the 1860s and 1870s by performers whom had lived in the 1820s and 1830s. That said, klezmer was hardly ever recorded or even transcribed as music prior to the 1920s, both because it was seen as "unserious" music but also because it's performers were a somewhat marginalized population, even within the insular worlds of the Yiddish shetl communities.
Most of the performers of the Eastern European styles of klezmer were mudered in the Holocaust, and many of their musical traditions died with them.
Modern 20th-century klezmer has two basic styles: American and Israeli-European. The American style is the one you, OP, are probably most familiar with, given your follow-up question about steel drums. The klezmer music the Ashkenazim whom immigrated to North America came into contact with, and was muturally influenced by, the contemporary dance-hall music of the early 1900s, and later by Jazz and Disco. The result was the adoption of Jazz elements like complexly syncopated beats, and Jazz-style instruments like the saxaphone, piano, and full drum kit, which had not previously been part of klezmer music.
Israeli-European Style Klezmer (not an official name!) is often considered more "authentic", but I personally disdain that as old-world snobbery. It's probably closer to the original 19th century styles, but also incorporates musical influences from Balkans brought by Sephardic Jewish musicans whom adopted klezmer as their own in cities like Salonika and later Tel Aviv.
The big names in contemporary schoarlship and performance of klezmer music (it's a small world) include Henry Sapoznik, Yale Strom, Mark Slobin, and Walter Zev Feldman. Anything they write is a good source on this subject.
In terms of further reading (and the books I've largely drawn on to write this answer), I especially reccomend the following:
Full disclosure: I have attended concerts by Dr. Feldman himself
If you have any followup questions, I'm happy to answer them, but its getting late and I need sleep.
Sorry, if its unanswerable... i guess steel drums and carribean music is a similar phenomenon.... but whats going on here?