"Cat among the pixies" - play on "cat among the pigeons," which is also the name of a Hercule Poirot novel by Agatha Cristie, meaning to do something to cause a lot of people bother or worry. Specifically, Arabella Figg's description of Mundungus Fletcher.
"Wasn't room to swing a Kneazle"- play on, "No room to swing a cat", meaning it is very cramped. Used by Rubeus Hagrid to describe the area where the giants lived.
"Fell off the back of a broom" - synonymous with "fell off the back of a lorry/truck," meaning stolen merchandise. Mundungus Fletcher leaves his shift of watching over Harry Potter to see to such items, in 1995.
"Get off his high hippogriff" - synonymous with "get off his high horse," meaning to stop being conceited - used by Rita Skeeter to describe Elphias Doge. A hippogriff is a magical creature resultng from mating a horse with a griffin, making it appropriate as a magical metaphor for a horse.
"Hanged for a dragon as an egg" - synonymous with "hanged for a sheep as a lamb;" if one is to be punished for committing minor offence anyway, one may as well go ahead with something even worse if it gets the job done better.
"Hold your hippogriffs" - synonymous with "hold your horses;" a request to wait for an explanation. Hippogriffs are magical creatures, and a more appropriate animal to use than a horse. Thestrals, unicorns or other creatures of a similar nature may have been used in earlier forms of the saying, however the slight alliteration has made this the most used.
"Royal hippogriff" - synonymous with "royal hypocrite," meaning that an assumption was made on the basis of a stereotype. Hippogriff is used because it sounds similar and is more appropriate to the wizarding world.
"It's no good crying over spilt potion" - synonymous with "It's no good crying over spilt milk," meaning it is no use worrying about unfortunate events which have already happened and which cannot be changed. Used by Arabella Figg.
"I wouldn't come near you with a ten-foot broomstick" - synonymous with "ten foot pole" in the Muggle world. Used in reference to someone or something that is considered unapproachable or offensive.
"Like bowtruckles on doxy eggs" - play on the Muggle phrase "like white on rice," which means to stick to someone or something very closely.
"Poisonous toadstools don't change their spots" - play on the Muggle phrase "a leopard can't change its spots," meaning that one can't change basic aspects of their character, particularly negative ones.
"The fire's lit, but the cauldron's empty"- play on the Muggle phrase "the lights are on, but nobody's home," meaning someone seems to function correctly, but is actually somewhat dim. Used by Ivor Dillonsby to describe Bathilda Bagshot.
"To have a hairy heart" - means to be cold and unfeeling. Derived from the Beedle the Bard story The Warlock's Hairy Heart, in which a wizard cuts out his heart and seals it away in a crystal box, causing it to grow hair.