Anika is a form of Annika , which again is a Swedish form of Anna , which again is a Latinate form of Hannah . Hannah means favour or grace
The first Annika which springs to my mind is the girl in the Books about Pipi Long Stocking. The boy and the girl she plays together with are at least in Swedish called Tommy and Annika . I have always found that there was something very gentle about Annika compared to Pipi, which is a rough and STRONG!, but also sensitive girl.
Anisha and Talisha do not means anything really as far as I know but the "sha" ending could be the same as the one in the name Sasha . The "ani" of Anisha must have been taken from a name such as Annika while the "tali" of Talisha must have been taken from the object called a Talisman.