Non re-usable nuts are torque nuts. There's all different types but the most common two are Elliptical and the Nylock style.
Elliptical nuts are deformed into an elliptical shape during manufacturing. When they're torqued onto the thread they retain a little of their shape and lock onto the thread, These types should always be replaced as they loose their original shape and wont lock the same a second time around, they can even weaken and break.
The Nylock style typically has a thread like a normal nut except at one end has a band of nylon which prevents the nut from backing off once torqued. Theres debate as to wether these can be reused or not. Some say yes, others no. I say it depends on quality and age of the nut.
Torque nuts generally don't need grease or locktite. You should only grease where the good book says to grease
