"Hagaane no Kuraku" is a pun meaning "Clark of Steel", a reference to Superman's titles of "Clark Kent" and "Man of Steel".
The brief retro sequence which Alfred shows Batman, is a tribute to campy 70's "Super Robot" cartoon, 'Science Ninja Team Gatchaman' (1972), which is better known in the West (slightly tweaked and dubbed into English) as 'Battle of the Planets' (1978).
While most characters are styled after either modern, or Edo period Yakuza, Joker and Harley Quinn have clothes and vehicles in the style of 'Bosozoku' ("Speed Tribe" or "Lightning Tribe") gangsters; A youth subculture of motorcycle gangs, that were common in Japan from the late 70's, to the 90's. Bosozoku gangs were teenage delinquents with a very unique look, that was a weird mix of influences, from Western "1%er" Outlaw MC's/biker gangs like Hells Angels, as well as western hip hop and raver culture, clothing/aesthetics from sci-fi media, and also Kamikaze fighter pilots from WW2. Harley Quinn's oddly-styled motorcycle is customised with several distinct, bosozoku elements.