So, for example, if Germany attacks Yugoslavia on G1 but does not conquer it, Yugoslavia is no longer neutral. Germany can’t fly air over Yugoslavia in the combat movement phase, but may attack Yugoslavia with aircraft. Then after not conquering Yugoslavia, Germany can freely fly aircraft over Yugoslavia in the noncombat phase, and any other power may fly over Yugoslavia. Also, any non-neutral Allied power may land aircraft in Yugoslavia to join the surviving infantry. Of course, this does not activate Yugoslavia, but the Allies are able to land there once it has been attacked.
It works the same way for strict neutrals.
A country is either neutral or it is not. Once it has been attacked by any unit, it is no longer neutral.