I'd go with VIE-ə-lə. I heard it that way once when I was a kid and liked it.
It reminds me of
Violet and
Ursula but seems more delicate. There's something about it that irritates me, though; it's like beautiful itchy lace.
vie-O-luh reminds me of the TV show Mama's Family and seems more dated, less refined.
I say the instrument viola like vee-oh-luh.