I'm not a linguist so I can't send any articles that explain the origins of this mess. But here are actual examples of usage:
dwa ptaki (two birds)
dwoje ludzi (two persons)
dwie dziewczyny (two girls)
idę z dwiema dziewczynami (I'm walking with two girls)
dałem kwiaty dwom dziewczynom (I gave flowers to two girls)
kanapa dla dwojga (a sofa for two - gender unspecified)
dałem śniadanie dwojgu (I served breakfast for two others)
dwójka to słaba ocena (two is a poor grade)
dwie dwójki to razem czwórka (two twos are four altogether)
dostałem dwójkę z Fizyki (I got a two in physics)
z dwójką przyjaciół poszliśmy do klubu (we went to the club with two friends)
w autobusie dwójce siedział pijany facet (there was a drunk fella on bus number two)
O, dwójko, nie wracaj już do mojego dziennika (Oh, two, don’t come back to my gradebook again)
Of course I don't consciously think about when to use the right conjugation. I just know it by heart and it's second nature but I can only give coherent rules to some of them.
> I'm not a linguist so I can't send any articles that explain the origins of this mess.
It's probably because Polish, unlike English and most Western European languages, has a case system (where nouns are modified to indicate their function, i.e subject, object, instrument, etc).
That's a pretty common feature in grammatically conservative Indo-European languages. Other living Indo-European languages, like Lithuanian, are even more conservative and have preserved nearly the entire case system of their ancestor.
dwa ptaki (two birds)
dwoje ludzi (two persons)
dwie dziewczyny (two girls)
idę z dwiema dziewczynami (I'm walking with two girls)
dałem kwiaty dwom dziewczynom (I gave flowers to two girls)
kanapa dla dwojga (a sofa for two - gender unspecified)
dałem śniadanie dwojgu (I served breakfast for two others)
dwójka to słaba ocena (two is a poor grade)
dwie dwójki to razem czwórka (two twos are four altogether)
dostałem dwójkę z Fizyki (I got a two in physics)
z dwójką przyjaciół poszliśmy do klubu (we went to the club with two friends)
w autobusie dwójce siedział pijany facet (there was a drunk fella on bus number two)
O, dwójko, nie wracaj już do mojego dziennika (Oh, two, don’t come back to my gradebook again)
Of course I don't consciously think about when to use the right conjugation. I just know it by heart and it's second nature but I can only give coherent rules to some of them.