"Both cats are black."
Translation:Oba koty są czarne.
Masculine personal is used only for... well, masculine persons. Cats are not persons.
It does, that's the point.
oba - masculine or neuter, but not personal. Oba psy, oba koty, oba domy, oba drzewa, oba pudełka.
obaj - masculine personal. Obaj chłopcy, obaj mężczyźni, obaj policjanci (two male policemen)
obie - feminine. Obie kobiety, obie dziewczynki, obie książki, obie sukienki.
oboje - two living creatures (both humans or one human and one animal) that differ in gender; or two living creatures (both humans or both animals), at least one of them being neuter
Obviously 'oboje' is the most problematic option. When you have "Adam i Ewa", they are 'oboje' without a doubt, just as "mężczyzna i kobieta". Also "Adam i jego pies" or "Ewa i jej kot" - also 'oboje'. "Parents" apply here as well, at least in Poland, as there are no same-sex couples with children here.
There are probably not many neuter nouns for living creatures, but "dziecko" is an obvious one, so "kobieta i dziecko" is 'oboje', and two children are also 'oboje dzieci'. As for animals, I suggest gnu: "tygrys i gnu" will be 'oboje' as well.
Obaj is a masculine form, not a mixed-gender one! Oboje is used when there are both males and females in the group.
Yeah, I guess you're right, the policemen example was wrong. Edited, thanks.
"obojga" is Genitive of "oboje"
"obydwa" is an alternative word for "oba". Similarly "obydwie" for "obie", "obydwaj" for "obaj" and "obydwoje" for "oboje".
They somehow show even more explicitly that the word is about 'two' of something.