His style mostly founds on the former Lightsaber Form V, also called Shien/Djem So (check the various Lightsaber Forms to get better insight - Craig Page wrote a quite interesting and informative essay about them). It's more or less the "signature form" for many of the Skywalker bloodline according to Legends. However, since Luke didn't receive any actual lightsaber training like the younglings did, he didn't know much about the different forms. I think he used it without really knowing its basics, acting more instinctively.
Hey thanks for the reply Racona Nova! I'll look into Form V.
Good point about him never being trained like a youngling. In that sense he'd be like a self-taught artist with a very natural aptitude vs. someone with years of formal training. The movies seem to imply that Ben/Obi-Wan taught him some basic moves but was really focused on getting Luke to learn how to stretch out and feel the living Force in the first place. Yoda later expanded on that and breaking down Luke's perceptions about what is and isn't possible while also teaching him the differences between the Light and Dark sides. Though not on camera I would imagine that some saber training was done ( think there might even be a deleted scene) but still very informal.