"fry off" = "fry". I worked in a kitchen and I heard "cook off", "fry off" quite a lot. The idea with "off" here is the completion of the task e.g. You should fry the steaks for 2 mins (don't say "off" or "up") e.g. You should fry off the steak (= fry them fully, as the recipe indicates, for as long as they need) I do not hear "fry up" as a verb but if it is used as a verb, I would guess that the meaning is "fry off". I hear "fry-up" as a noun. In the UK, a "fry-up" is a dish - usually breakfast - composed of fried food e.g. bacon, sausage, mushroom, tomatoes, etc.

Fry and fry up both mean to fry something. But fry up is more casual and informal. Fry off: I don't have context, but I assume it's two or more cooks battling each other for who fries something the best...like a frying contest