Suffixing by "-rama", "-orama" or "-arama" — how did this begin?

Etymonline to the rescue:

-rama noun suffix meaning "spectacular display or instance of," 1824, abstracted from panorama, ultimately from Greek horama [ὅραμα] "sight."

Briefly, diorama and panorama were popular in Napoleonic times, if not before, and came into and out of fashion as such words do. Specifically, they enjoyed a vogue after WW2, when film-makers were looking for impressive names for their colour and widescreen films (Colorama, Futurama, Technorama, etc- probably influenced by drama, but not directly connected). The vogue led to many bottle stores, for example, renaming themselves liquoramas to draw in customers, though there is no plausible meaning for this, let alone etymology. Mercifully, the fashion seems to have died away.
(Thanks to The Straight Dope, as referenced above: but their article's too long to quote directly).

There's a long article on this on The Straight Dope, here: https://www.straightdope.com/21341675/where-does-the-suffix-arama-as-in-foodarama-come-from

Summarizing: Originally derives from “panorama” (from the Greek pan, all, plus horama, view). The -arama suffix was then attached to a lot more words (cinorama, diorama, etc.) forming a pattern, which eventually led to -arama being attached to cinema processes, etc.

This is a bad summary, please read the article :)