In the early episodes of the first season when the youma were destroyed they did not say anything. After Sailor Moon began using Moon Healing Escalation the youma would say "Refresh!" when they were destroyed.
Any monster sent by Jadeite is usually in a human disguise (often impersonating someone else), to help Jadeite attach his items (which are charged with dark energy) to people to steal the energy from them. Most are killed by Sailor Moon, but at least one is killed by Sailor Mars.
As Nephrite works by finding a person whose energy is about to reach its peak, he will usually charge it with dark energy and then when the person's energy reaches its peak, a monster will come out while the person ends up unconscious. The victim returns to normal when the monster is destroyed.
It is important to note that the Soul Shadow is not a youma per-se but rather an apparition of Nephrite. It is also interesting to note that Regulus and Soul Shadow (interestingly enough, the only two male servants of Nephrite) were not summoned the same way as the others, nor were they involved in an energy-absorbing plot.
Zoisite has at least four regular monsters working for him, but after Nephrite dies, and Zoisite takes over, his task is to reawaken the Seven Great Youma inside people who carry the Rainbow Crystals. Thus, whenever he takes a crystal, he transforms them into a monster, which in the "Rainbow Crystal Carriers" case, is the Shadow within them. He can also change other people into monsters, as shown when he does this to an actor. To destroy the Seven Great Youma and heal the victims, Sailor Moon must use her Moon Healing Escalation on them.
Seven Great Youma
The Seven Great Youma were the most powerful monsters of the Dark Kingdom. They were defeated and trapped inside the seven Rainbow Crystals, disappearing into the Earth's atmosphere. Each of them, as well as a crystal, went inside a specific person (one of them inside a cat). One by one, Zoisite awakened them by transforming the person carrying the crystal into a monster, but each Shadow was destroyed when the monsters were healed by Sailor Moon.
Youma Created by Zoisite
Like Zoisite, Kunzite usually works by changing innocent people into youma, where Sailor Moon must heal them. At one point, he turns several people into monsters at once. When he transforms Misha and Janelyn, they retain their original names. Unlike Zoisite, whose task was to collect the crystals, Kunzite's objective (and therefore the objective of his monster-victims as well) is purely to find and destroy Sailor Moon. The difference from the victims Zoisite turned into monsters is that Kunzite's monsters can resume their human forms whenever they want (though they remain evil until they are healed by Sailor Moon's Moon Healing Escalation).
Unlike the manga, most of the youma in Pretty Guardian Sailor Moon did not have names and were summoned in an inconsistent manner. Some of them were created from stones that were infused into objects, which turned the object into a youma, others were simply summoned. After Queen Metalia's power began to grow in reaction to the Silver Crystal's power, a new type of youma were created. The new youma were all identical to each other, were weaker than previous ones and only appeared together in groups. In Act 41, Metalia also summoned a single youma which drained energy from people throughout Tokyo, leaving them comatose. In Act 45, Metalia herself controlled this youma, but was forced back out by Sailor Venus before Sailor Moon destroyed it. In the Final Act, Princess Sailor Moon summoned a group of white youma to slow down the Sailor Senshi so they could not stop her from her plan to destroy the Earth. In the Special Act, Queen Mio summoned two Youma, Sword and Shield, two youma that had actual names. Along with them, she also used a group of clown-like Youma called "Pierrot." Queen Mio turns into a youma in special act.
In Sera Myu
In the musical Gaiden Dark Kingdom Fukkatsu Hen and its revision, there was a youma named Manegin who disguised herself as Haruna Sakurada. Manegin also had control of other youma who acted under her control. Manegin, along with the DD girls who were in the first two musicals, reappeared in the Sailor Moon Super Spring Festival.
In Video Games
In the video game Sailor Moon for Super Famicom, there were three original youma characters designed by Naoko Takeuchi: HiraHira, MuchiMuchi, and GoroGoro. In Sailor Moon for the Mega Drive Manegin reappeared.