The 36 master poets are here: http://100poets.wordpress.com/the-36-immortals-of-poetry/, and are listed on wikipedia here – and they are simply selected poets of the Heian era in Japan.
I don’t know why people refer to this woodblock print as being related to the to the 三十六歌仙 Sanjūrokkasen (36 immortals) because they are in fact two different expressions.
三十六河川 = sanjūroku kasen and this means: “36 river antics”—which makes a lot more sense with the pictures on the original wood block. It is definitely in some (non-standard Japanese) dialect – probably Hama-kotoba (浜言葉, essentially seashore slang) – as that is what was spoken in Kanagawa—the area where Perry landed (he landed in Yokosuka in 1853) (along with early Kanto-ben) back in the 1800s. Info on Perry’s landing and the Kanagawa Convention here and here.
Anyways, the best information about this item is listed with its call number at the Library of Congress – where this item now lives after having been donated by Emily Crane Chadbourne in the 1930s. (...And if you’re interested in her back-story and how Emily happened to be such a well-traveled art collector, a good article to start with in PDF format is here).
I can’t hope to translate this calligraphy from this wood block print – because aside from the fact that its calligraphy (so I can only make out some of the standard kanji and a few distinct hiragana characters – mostly grammatical bits) I know no Kanto-ben and certainly even less about Hama-kotoba.
I lived in the south of Japan so I know only bits and pieces of Ryuku-dialect and more than the average amount of Oita-ben (which frankly, just amuses most Japanese I meet…because speakers of Oita-ben are few and far between.)
Anyways, I would dispute that there is any connection between this woodblock print and the 36 master poets. I don’t get that from it at all.
This looks instead like a woodblock print that was meant to be humorous/satire and dates to the 1850s. (The artist of this print is unknown.) Woodblock prints were the common medium of the period between 1800 and 1899 in Japan. A really good online book where you can see many well-known artists and publishers of these woodblock prints is located here.