Damn, this is getting complicated (and I thought it was complicated in Chinese!). OK to differentiate, you could say as Seth suggested, my paternal aunt/uncle (or "my aunt/uncle on my father's side"), my maternal aunt (or "my aunt/uncle on my mother's side"). To further differentiate, you could say my Aunt Sally, my mom's younger/older sister or my Uncle John, my dad's older sister's husband. You could also differentiate whether this person is your aunt/uncle through birth or marriage by saying "my aunt, by blood" (meaning this is your mother or father's sister, not their brother's wife). In practice thank God, we rarely say anything other than "my aunt" or "my uncle".

Maybe using the adjectives "paternal" (father's brothers and sisters in this case) and "maternal" (mother's brother's and sisters in this case) you can find a way to translate. "paternal aunt" "paternal uncle" "maternal aunt" "maternal uncle"