Why does the case change when I mention my family?

I’m a heritage learner trying to speak more naturally with my grandmother, but every time I try to talk about 'my father' or 'my brother', I get lost in the case endings. Why does 'otac' change to 'oca' or 'ocu' depending on the sentence? I want to sound authentic rather than stiff—are there any shortcut patterns for talking about family in Serbian that don't require me to memorize the entire declension table before I open my mouth?