"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".
Update: of course both "так" and "як" are valid Ukrainian words and they can be near each other in a sentence e. g. "Якщо все написано так, як і хотілося, то можна сміливо писати твір у зошит", but I can't imagine a sentence where there is no coma between them, and in any case they will be totally separate words.
