I want to move nodes precisely but the changes are ignored if the distance is not very large. Snapping is completely off, I tried to set the nudge distance to minimal values (even 0,0), raised the scaling but nothing helps.
That usually happens when the node's position is being controlled by something else. Depending on the software, it could be due to auto-layout, constraints, a parent object, or a locked node. I'd check whether the node is locked, disable any automatic arrangement features, and make sure you're in the correct edit mode before moving it. Which application are you using?