I like the Spanish invented, imprecise numbers. I wonder how they are in different languages.

For example, we have:

Un puñado (a handful, "puño" is the closed hand)
dieci... (10+?) (diecimuchos (10 + a lot), diecipocos (10+ a few), etc). Same with venti... (20+), treintay... (30+?) etc.
taytantos (30 to 99)
EDIT: cienes y cienes (several hundreds, a joke/malformation of the correct "cientos y cientos" (hundreds and hundreds))
tropecientos (several, many hundreds)
miles y miles (thousands and thousands, up to 99,999 I suppose)
tropecientosmil (several, many hundred thousands (up to 1 million, I suppose)
millones y millones (millions and millions)
tropecientosmil millones (many hundred thousand millions).
From here, you just change "millones" (millions) for billones, trillones, or whatever.
I also like to say "dos, o tres... cientos", "two, or three... hundreds" which is a number much higher than expected (expected 2-3, but real number is between 2 and 300). But this is a joke, I suppose it's not standard Spanish.
EDIT2: there's also "chorrocientas" or "chorrecientas" which is several hundreds, same as "tropecientas"

In English, I know "a handful", "zillion" and "gazillion" but I don't know any other. Do they exist? What about in other languages?

There is a very nice tale from Gianni Rodari, "A inventare i numeri", I've read it (in Spanish) with my son several times, he doesn't like it very much (maybe it's early for him) but I like it a lot.