This is Bulma alone complaining about Goku rudeness. Translated as: "I can't believe he had the nerve to call me stuff like witch or fairy".
人のことを = things to people (like in saying things to people)
魔法使いだ = I'm a witch
とか = listing (incomplete)
妖怪だ = I'm a fairy/demon
と = nominalizer
いっとき = ?? (I guess some form of いい)
ながら = while
言っとき【いっとき】 is a colloquial contraction of 言っておき, where this おき is the masu-stem of おく, which is a subsidiary verb that adds the nuance of "leaving the resultant state". See this question, this chart and this article.
This 人のこと is closer to "things about someone" rather than "things to people" (see this). This 言う is using the A + を + B(だ) + と + verb pattern (see this and this). Note that this と is not a nominalizer but a particle close in purpose to English "as". Thus 人のことを魔法使いだと言う effectively means "to call someone a witch", and the 人 refers to "me" in this context. A literal translation would look like this:
人のことを魔法使いだとか妖怪だといっときながら
While having called me a witch or a monster, he...!
He's said I was a witch or I was a monster (and has never corrected that), and still...!
The part after ながら is left out, but something bad about Goku is expected. (Perhaps something related to his ignorance about his own abnormality? Depends on the story.) That's where "had the nerve" came from.
