I use the Crystal Crown quite often when I want to speed up skilling, fame or career leveling for my super sims. The hematite crystal recharges the fun need & boosts job performance which helps my Sims get promoted faster. The diamond crystal recharges social need & boosts fame gains. Certain crystals also give skill boosts when in the crown:
Crandestine (Get to Work) recharges all needs except energy & boosts painting/writing/creativity skills
Amazonite (Jungle Adventure) boosts the archeology & mental skill & recharges all needs except hunger
Amethyst recharges hunger need & boosts logic & mental skill
Jonquilist fills needs except energy & boosts charisma & social skill
Plumbite fills needs except energy & boosts fitness & motor skill
However, for faster skilling I generally just use a peach crystal in the crown (which keeps a Sims bladder need full) then I have the Sim drink snaggle fluster (& if the Sim has access, they also drink a potion of Nimble Mind) prior to working on a skill for a large boost.
Here's a good list of crystals & their effects: https://sims.fandom.com/wiki/Celestial_Crystal_Crown
I use the weather machine occasionally (most often to prevent rain during Geek Con).
I generally only use the Omiscan relics in order to complete the Jungle Explorer aspiration & to summon the skeleton assistant.
I have tried the freeze ray function of the Sim Ray. But, I haven't tried the other features yet.
I have not used the other objects yet.
