Prince Charles's father is the Duke of Edinburgh, who was formerly Prince Philip of Greece. However, the Greek royal family is not of Greek blood. Philip's father, Andrew of Greece was of Oldenburg blood, which was a Danish noble family, and Philip's mother was Alice of Battenberg, who was German. There is some Russian noble blood intermarried with the Oldenburg's, but as far as I know, the only Oldenburg who married a Greek was Marie of Greece, and she was not an ancestress of Philip.
The connexion with the Spanish royal family is similar: King Juan Carlos's queen is Sofia, the daughter of Paul I of Greece, who was also an Oldenburg. Her mother was Frederica of Hanover, who was, of course, German.
To say that Elizabeth II has ties with the Hanovers is an understatement: she is a direct descendant of the Hanover royal family of England. The name of the royal family was changed from Saxe-Coburg-Gotha to Windsor during WWI to veil the German heritage, and Edward VII Saxe-Coburg-Gotha was the son of Queen Victoria and Prince Albert. You can't get much more German than that!