In Sweden, it is pronounced UNN-ee-kah (or ONN-ee-kah), it is hard to describe without a phonetic alphabet. The big difference is in the pronounciation of the first A.
I think
Annika is originally Dutch (
Anneke) but I'm not sure how it is pronounced there.
I think that I myself would pronounce it as ANN-ick-a if I went to USA, but I don't know which pronounciation is considered "correct" in USA.