売り切れ and 完売 roughly mean the same thing, "sold out". We commonly see both 売り切れ and 完売 on a signboard. When asking a store clerk, you can say either Xは売り切れですか or Xは完売ですか. The difference is not large, but 完売 sounds more technical because it's a Sino-Japanese word. 売り切れ is probably more common in speech.
売り切り means something different. Its meaning depends on the context, but the basic underlying meaning is "once we've sold it, that's the end". For example, 売り切りの商品 means an item that won't be restocked. 売り切りのゲーム refers to a package game as opposed to an online game with monthly billing system. It can also refers to bargain/sale/clearance.