Kvazery probably stays for the multiplicity of quasi-something movements.

Lyudokhody - those who are going "v lyudi", into the world (the very well-known work of Gorky - sort of autobiography - was called "V lyudyakh" and was about the harsh life of the young writer-to-be doing all kinds of jobs to survive.

Nichevoki (ничевоки) rings a bell for me although I never was much interested what they were exactly busy with.

Pustogloty - either those who could not speak any language properly, or those who had /wanted nothing to eat / swallow? (Glotat' means to swallow), or somebody who were leading emply (and/or loud) talks (from glotka глотка - gullet, throat; there is an expression орать во всю глотку - cry at the top of one's voice.

Just some comments on the possible translations of the cryptic names of
some real or imaginary literary groups from the text; I do not know what
groups or movements, if any, Bykov is hinting at, so I am just
speculating from what I think the meaning of the name might be.

"людоходы" and the googled-up photograph: I don't think the word is
related to what the photograph's title hints at -- the photograph is
likely comparing the chaotic movement of people on the square with
"ледоход" (thawing of ice on a river in spring producing chaotic
ice-plate movement); "людоход" as a title hints at "ледоход", I believe.
As for the supposed literary group's name
"людоходы", it is probably related to the expression "пойти/ходить в
люди" or "ходить в народ", so the group's name might point to some sort
of literary populism (those going out to the people, populists).

"квазеры": likely hinting at the prefix "квази-" ("quasi-", almost), and
probably means some sort of imitation; another example of an artificial
word constructed in this way would be "псевдоквазия" ("pseudo-quasia",
invented word that is supposed to mean deceptive imitation) -- I remember
it used in one of Strugatsky brothers' novels.

Thanks very much—you're both obviously right about людоходы and квазеры, and I'll change the translation accordingly.

Actually, "ничевоки", mentioned by Ashalynd, are real and -- probably -- relevant, as quick googling shows:

http://feb-web.ru/feb/litenc/encyclop/le8/le8-1081.htm

As for "аквилеги", this link to a Russian translation of Seneca:

http://www.centant.pu.ru/sno/projects/seneca/naturales_quaest3.htm

mentions the name in its footnotes as that of the "ancient Roman corporation of water-finders"...

Thanks! Here's the direct nichevoki link: "Н. провозгласили «отделение искусства от государства», а свое творческое бюро выдвигали в качестве аппарата по руководству искусством. Н. выявили себя откровенно буржуазной, враждебной революции, пролетарской диктатуре группировкой, оспаривавшей принципы культурного строительства пролетариата. В литературе Н. не оставили никакого следа..." They sound like a perfect group for this novel!

Another thought: "квазеры", I would venture to suggest, might be an anachronism, and so a mistake by Bykov if it's indeed invented. I believe the more likely form, for 1920s, would be "квазёры" or "квазисты" ("акмеисты" being a case in point) -- this is supposed to be happening before the onslaught of English-inspired neologisms, after all...

Or is it just a case of "ё" replaced by "e" -- maybe it was "квазёры" all along, and, then, a word that immediately invoked, by the sound of it, the word "фразёры", "(empty, useless) phrase-crackers"(?). The latter is probably a bit far-fetched, though.

I believe that "ушкуйники" here refers to the poetry almanac and possibly to the corresponding group of poets:

ЧУКОВСКИЙ, НИКОЛАЙ КОРНЕЕВИЧ (1904–1965), русский писатель, переводчик. Сын К.И.Чуковского.[..]Начал выступать со стихами в 1922 в альманахе Ушкуйники (Петроград), изданном Чуковским за собственный счет (под псевд. Н.Радищев), в литературном приложении к берлинской газете «Накануне» (4 июня) и петроградском журнале «Современное обозрение» (№ 2).
http://www.krugosvet.ru/articles/67/1006788/1006788a1.htm

"pustoglots" makes me think of The Puszta, so my instinct (wrong as it may be) would be to say that it means "speakers of the plains dialect".