"Позаяк" is a bit rare word and some Ukrainian-speaking people might not understand it, but it means "because".
Most people will understand "так як" as "because", but it is just wrong literal translation from Russian "так как" (as you can see, for example, in this list of common mistakes).
More common words for "because" are: "бо", "оскільки", "адже", "тому що".
But feel free to use "позаяк": it currently gains popularity back :)
Example:
Позаяк цікавого не маю що писати, тягтиму далі свою подорож, хоч, може, вона тобі теж не цікава (Михайло Коцюбинський, III, 1956, 140) (first example from СУМ)
Quick translation: "As I don't have anything interesting to write I'll just continue our journey though it isn't interesting to you too".
