They do for most nouns, but the masculine personal takes Genitive anyway. Well, 2/3/4 have two equally correct forms each, one of them takes Nominative and the other takes Genitive.
[Dwaj/Trzej/Czterej] mężczyźni piją piwo. (Nominative)
[Dwóch/Trzech/Czterech] mężczyzn pije piwo. (Genitive)
And then for other numerals, masculine personal needs a Genitive form of the numeral and Genitive form of the noun.
(I am wondering if masculine personal of "22" can be "dwadzieścia dwaj", but I'm almost sure it's wrong. "dwudziestu dwóch" is definitely correct.)
Welcome to Polish numerals, where even natives that teach it may have problems sometimes.
So, the form "sto" for sto is only used in two cases (or three): nom./voc. "non-masculine" and accusative "non-masculine?" Every other time it is actually "stu" including all invocations of the genitive, dative, instrumental, and locative cases, and the masculine-personal invocations of the nominative and vocative cases?
It makes one wonder why the word is even listed as "sto" in the dictionary, rather than "stu."
Ok the stu was a bit frustrating; really caught me off guard. Numbers are hard enough for me and your explanation to odwl is helpful but declining numbers and numbers in general could be a tree unto itself as far as I am concerned. I hope there will be lots more number exercises in the new tree or maybe break out lessons.
Please look here: https://ell.stackexchange.com/questions/923/difference-between-hundred-a-hundred-and-one-hundred It seems that, to only say the numeral without "a" or "one (or two, three...etc)" in front of it (depending on whether the exact number is important or not), is grammatically wrong.
It's a "WONKY" answer. Nobody english would write this. Either it's a hundred or one hundred. A 100 men= a one hundred men and doesn't work unless you say something like " I have a 100 dollar bill where 100 is used as an adjective ( describing the kind of money bill it is). A hundred men and a hundred women. or 100 men and 100 women. :))