Yikes! What a pair have we here! The first might look like a typo for yolk, but the second looks like a plural of the first but with the addition of a c. They also may bring to mind yoink, a slang term for “steal”, and yonks, meaning “a long time” (as in “I haven’t seen him for yonks!”).
At any rate, the words seem suited to a high-sharp shout – which is what yoicks is, really: a shout in fox hunting to encourage the hounds. Apparently the sound of yoicks really gets the dogs going. It is thought to have come from hike. It can also be used as a non-dog-related shout of encouragement or exultation.
Yoik, on the other hand, sometimes seen as yoick but also seen as joik (or even joiggus or joiku), is a kind of song. Some of it may involve sharp, high shouts, but mostly it sounds to many ears more like Native American songs. If you guessed from the spelling joik that the source is actually northern Europe, however, you’re right: specifically, the Saami, who live in Scandinavia. They speak Finno-Ugric languages (thus related to Finnish and Estonian and, more distantly, to Hungarian) – actually about ten different languages. They were traditionally reindeer herders, and some still are; their nomadic lifestyle led them often to live in portable residences that will look to many eyes very much like teepees. And because they got to northern Scandinavia first, they are considered the indigenous people of the area – one might say autochthonous: belonging to the land. Which seems, unfortunately, to have resulted in their being treated like dirt, historically, after the north Germanic people landed in their laps. (Oh, laps: the Saami are often called Lapps or even Laplanders. They would rather be called Saami.)
Anyway, yoik is sometimes used to refer to any Saami song, but it is often more specifically referring to the luohti song of the North Saami, a song that aims to communicate the essence of an individual person or place. It often has a repetitive, chanting kind of sound, and the text itself is often elliptical and has many nonlexical syllables. It can often be heard performed with more modern instrumentation and arrangements now; I was first made aware of it by the music of Mari Boine. See www.youtube.com/watch?v=KbEfoOMlo4Y for a yoik from her with images of the Saami and their native land. (For more in-depth information on yoiks, see www.fimic.fi.)
I’ll take a yoik over yoicks – so much more durably exalting to my ears, and not at all gone to the dogs.