the Oak Leaves clasp could be awarded for leadership, distinguished service or personal gallantry. But i can find anything about the other ones.
Knight's Cross: Knight's Cross with Oak Leaves: Knight's Cross with Oak Leaves and Swords: Knight's Cross with Oak Leaves, Swords and Diamonds: Knight's Cross with Golden Oak Leaves, Swords and Diamonds: Grand Cross of the Iron Cross: Star of the Grand Cross of the Iron Cross:
Edit: Reddit makes the copy template look like its next to each other very sorry. Edit: Germany gives out a diffrent type of iron crosses now. Do these have the same grades?
The Knights Cross was instituted on September 1st 1939 (7361 awarded during the war)
The Oak Leaves was instituted on June 3rd 1940 (890 awarded during the war)
Oak Leaves and Swords was instituted on September 28th 1941 (160 awarded during the war)
Oak Leaves, Swords, and Diamonds was instituted on September 28th 1941 (27 awarded during the war)
Golden Oak Leaves, Swords, and Diamonds was instituted on December 29th 1944 (1 awarded during the war)
Grand Cross of the Iron Cross was instituted on September 1st 1939 (1 awarded during the war)
Star of the Grand Cross of the Iron Cross (none awarded.)
The additional decorations were awarded for continuing service/gallantry.
For example, the award criteria for the Luftwaffe awarded points depending on the aircraft shot down: 1 point for a single engine plane, 2 points for a twin engine and 3 points for a four engine. The points were doubled if the action occurred at night. Initially, the Knights Cross was awarded at 20 points (plus the requirement of having been awarded the Iron Cross), the oak leaves would be awarded for a further 20 points and so on. The number of points required increased over the course of the war.
In the Kriegsmarine, the award was based on tonnage sunk (beginning with 100,000 tonnes initially) and additional awards would be made based on continued tonnage sunk.
The Golden Oak Leaves award was initally only to be awarded to 12 officers or men after a German victory. In practice it was awarded once to Stuka pilot Hans Rudel in January 1945.
The Grand Cross of the Iron Cross (which similar to the WWI award could only be awarded to generals) was only awarded once to Goering for the Luftwaffe campaign in France in 1940.
The Star of the Grand Cross was also reintroduced but never awarded (Goering had plans to award it to Hitler upon victory). There are only two prior recipients Blucher (for Waterloo) and Hindenburg (for the Battle of Tannenberg)
Sources:
G. Williamson: The Iron Cross, A History 1813-1957
G. Williamson: Knights Cross of the Iron Cross, A History 1939-1945
W. Fellgiebel: Die Träger des Ritterkreuzes des Eisernen Kreuzes 1939–1945
V. Scherzer: Die Ritterkreuzträger 1939–1945 Die Inhaber des Ritterkreuzes des Eisernen Kreuzes 1939 von Heer, Luftwaffe, Kriegsmarine, Waffen-SS, Volkssturm sowie mit Deutschland verbündeter Streitkräfte nach den Unterlagen des Bundesarchives