From personal experience Amethyst is generally used for channeling psychic energies. It's used to flow creativity and create a healthy and intuitive sleep (ie: through dreams.) It is a calming energy. Yes, it's also used in chakra work. It is a very psychic stone and is good if you are after channeling the spirits.
Onyx is more of a banishing stone. It is used to keep negative energy at bay. It is associated with the earth element.
Green Calcite, as with any green stone... Generally is used for luck and prosperity. Good to have around when financial planning (IMG:
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Tigers Eye I personally do not usually work with as it's not heavily used in Dream Majick or divination HOWEVER it's an earth based stone. Used for breaking curses and relieving stress and weariness. It's used in Africa for warding off black majick and ye' olde "EVIL EYE"
Pyrite (Fools Gold! Hah!) I have not worked with this one either (but after research maybe I should!) it's another banishing stone however unlike most sheild stones it harnesses the energy of the light and the sun rather than being heavily grounded in the earth element. It's used to promote intelligence and increase physical stamina whilst warding away particularly nasty negative energies.
If you are after encouraging spirits to enter your home and join you at night Amethyst is probably the best one to have around (And keeep the Onyx and the Fools Gold handy!)
If you are worried about spirits entering BECAUSE of the stones you can just ground them and protect them with the ol' salt circle or passing through white smoke trick!
Hope I helped.