Gems are used to get temporary boosts, and also combine well with the move Acrobatics and the ability Unburden.
Acrobatics: a 55 BP Flying-type attack that doubles in power when the user is not holding an Item. How does a Gem affect this? Simple: The boost from a Flying Gem activates before the doubling effect of Acrobatics. More simply, Acrobatics gets the boost from the Flying Gem, then the damage boost from not holding a item, turning a mediocre attack into a nuclear bomb. Unfortunately, this strategy is no longer legal, as the Flying Gem was only available in BW/BW2.
Unburden is an ability that gives the user a speed boost after its item has been consumed. This allows a sweeper (I'll use Sceptile) to get off one powerful boosted attack, then get a boost in speed and wreck things. This ability allows Sceptile to get two buffs, as opposed to just one when holding a Plate or other perma-boost items.
Acrobatics AND Unburden
The jewel of Gem movesets, being able to get an Acrobatics boost and activate Unburden. Only six Pokémon can do this: Sceptile and its pre-evos, Hawlucha, Drifloon and Drifblim. This is THE best strategy when using Gems. Honorable mentions go to Fighting Gem Terrakion, Flying Gem Talonflame, and Normal Gem ExtremeSpeed.
I hope that answers you question about Gems. Please note that Gems should only be used for competitive purposes, as they are single-use. For in-game, any of the items you listed would be better, as they are indefinite.