who created great suicidal dramas on the apartment cliff-banks of the Hudson under the wartime blue floodlight of the moon & their heads shall be crowned with laurel in oblivion,
They considered killing themselves by jumping off an apartment building.
To be "crowned with laurel" means to place a wreath of laurel leaves on someone's head after some big accomplishment, such as writing a great poem or winning a race. The idea goes back to Ancient Greece and Rome. The speaker ironically states that they would be praised as heroes if they committed suicide.
who ate the lamb stew of the imagination or digested the crab at the muddy bottom of the rivers of Bowery,
The Bowery is another neighborhood in New York. At that time, it was a slum. Today, it's in the hip and high-priced East Village.
The speaker seems to be suggesting that they had to eat imaginary lamb or some toxic-sounding crab because they could not afford real food.
who wept at the romance of the streets with their pushcarts full of onions and bad music,
They were homeless people wheeling shopping carts around the city. The carts were filled with onions (a cheap – and unsatisfying – source of food) and "bad music."
They cried about how romantic the streets looked.
who sat in boxes breathing in the darkness under the bridge, and rose up to build harpsichords in their lofts,
They started out so poor they had to live in a box underneath a bridge, but they "rose up" to have enough money to afford a small apartment where they built musical instruments.
The harpsichord is like a piano, except its strings are plucked instead of hammered.
who coughed on the sixth floor of Harlem crowned with flame under the tubercular sky surrounded by orange crates of theology,
They are sick, possibly with tuberculosis, which causes fits of coughing. Tuberculosis causes people to cough up blood, so a "tubercular sky" would probably be red or reddish orange. It could be sunset.