Say it in Polish, then reveal the answer.
Every reading above comes out of these. Learn them and the clock stops being arithmetic.
On the hour it is just the ordinal, in the feminine, because godzina — hour — is a feminine noun.
Up to the half hour you count forwards, and po puts the hour into the locative: siódma becomes siódmej.
The half hour looks ahead, not back. Polish says half to the next hour where English says half past the last one.
After the half hour you count down to the hour that is coming, and it returns to the nominative: ósma.
Watch Your Language is an iPhone and Apple Watch app for vocabulary. It puts the words you are learning in a widget on your Lock Screen and on your watch face, a few at a time, and brings back the ones you keep forgetting — including the numbers and time words this drill runs on: