You've over-simplified things. In fact your advice is wrong.
obaj - both males
Park is a masculine noun, but you CANNOT say
*obaj parkiObaj is used by all masculine personal nouns (
rzeczowniki męskoosobowe in Polish), used only for describing people.
ex:
obaj nauczyciele, obaj panowie, obaj Polacy, obaj koledzyobie - both females
This is correct.
Obie is used for all female nouns (
rzeczowniki żeńskie in Polish).
ex:
obie nauczycielki, obie panie, obie Polki, obie koleżanki, obie książkioboje - both male and female
This is over-simplified. You use
oboje when there is a group of two people, one male, one female. It's also politically correct to say for example:
oboje studentów instead of
obaj studenci, because you're not specifying that the two students are masculine.
Also
oboje is used with nouns such as
drzwi (door),
spodnie (pants),
nożyce (scissors),
sanie (sled) that have no singular form and always appear in the plural, even though the meaning is singular. In grammar these are known by the Latin term pluralia tantum.
One last usage for
oboje is for young beings (mostly animals)
ex:
oboje kurcząt (chicks),
oboje kociąt (kittens),
oboje dzieci (children)
Note that in all instances of
oboje + a noun the noun is in the Genitive case (
dopełniacz), whereas
obaj/obie/oba + noun the noun is in the Nominative (
mianownik)
oba - both things (neutral nouns)
This is half right.
Oba is used only for neuter (neutral is incorrect) nouns not described above. ex:
oba drzewa (trees),
oba imiona (names).
It's also used for masculine non-personal nouns. ex:
oba koty (cats),
oba widelce (forks),
oba budynki (buildings)