Learn Polish: Nieźle mówisz po polsku! - You speak Polish pretty well!

In Polish, nieźle (literally not badly) is often used as a very genuine, warm compliment rather than a reluctant okay. Native speakers frequently prefer it over bardzo dobrze to sound natural and casually impressed. It carries the meaning of pretty well or quite impressively.

I have used the po polsku phrase since day one, but grammatically speaking, what case is polsku in?

It is actually a remnant of an old, archaic case ending! In modern Polish, the preposition po usually takes the locative case (which would make the adjective polskim). However, for languages and a few other fixed phrases, Polish kept the ancient dative/locative ending -ku. So po polsku functions as a fixed adverbial phrase today.

Could I change the word order to Mówisz po polsku nieźle!?

You could, but putting nieźle at the very beginning places the emphasis exactly on the quality of the speech. By saying Nieźle mówisz, you are highlighting your positive impression right from the first word. Moving it to the end makes the compliment sound a bit flatter or like an afterthought.