I was wondering because their have been so many events in Japanese history that could erase these clans and their descendants, such as the Meiji Restoration and even World War Two. Thanks.
After the Meiji restoration, the clans were converted into noble families, along the lines of European nobility. Their domains were converted into prefectures, with a centralized authority, though they were allowed to keep 10% of the province's revenue. If you're interested in this time period, there's a great biography of Saigo called (unfortunately, due to the horrible Tom Cruise Movie) The Last Samurai, by Mark Ravina. It's a really good read.
The nobility was finally eliminated in 1947, though their descendents continued to do pretty well for themselves. (This book is pretty much exactly what you're looking for.) After WWII, they maintained an elitist status, referring to non-former-nobles who became rich as nariagari (upstarts) or narikin (nouveau riche). They were criticized for being ostentatious with their wealth (austerity was a virtue in old money families, with many boasting their maids wore better kimono than their own daughters).
According to popular belief, The Meiji Restoration was an effective wipe out of samurai nobility. Instead, the surviving samurai heads (that is, the heads of all the major clans excluding the Hojo, Takeda and Chosokabe) accepted the new order of the emperor. The 15th shogun of the Tokugawa shogunate, Tokugawa Yoshinobu, wanted to reform the shogunate and began the Boshin War, which also marks the beginning of the Meiji Restoration. Following the shogun's surrender and resignation, he retired and disappeared from public view for the majority of his later life. While the Emperor allowed him to create his own house for his family, his descendants do not retain the influence of their clan.
Oda Nobunaga's death at Honno-ji by the hands of his general Akechi Mitsuhide was the start of the end of the Oda clan. Central Japan soon fell into the control of another general, Toyotomi Hideyoshi. This left no substantial record available to prove bloodline, similar to many other clans that existed before the Meiji Restoration.
While there have been many claims of relationship to the major clans, another note to bear in mind is that over a long period families tend to create a new name for themselves after a fall from grace or due to an unknown heritage - a good example of this is the widespread family name of Takeda and Suzuki.