Spells (not to be confused with Spelling) are actions performed by a wizard or witch, sometimes with a wand or by wandless incantation, whether aloud or silently.
Spells can be used for a variety of purposes, good or bad, and can vary from simply levitating an object, stunning a person, or even killing them. In the original Harry Potter universe they were usually divided into several categories: Transfiguration, Charm, Jinx, Hex, Curse, Counter-Spell, and Healing. Curses are considered part of the school of Dark Magic, and are generally forbidden from use; at Hogwarts, students in the Defense Against the Dark Arts class would only learn how to defend against them, not to cast them at will.
In the My Immortal universe, all canonical understanding of spells and how students of magic interact with them goes right out the window - so does the spelling. In order to make sense of this mess, let's look at the various kinds of spells as Tara Gilesbie interprets them.
Transformation
Transformation (also spelled "Transfomation") spells involve (as the name suggests) changing from one form to another. An entire class at Hogwarts teaches the subject, and is first mentioned in Chapter 18. Transformation itself is hinted at in Chapter 15, where Ebony turns a bloody pentagram into a black guitar, and then the guitar transforms into Draco. This chapter likewise suggests that Transformation is also called "Biology class," and that Loopin is the Transformation professor.
Difference from the Original
Transformation is based off of Transfiguration, which was taught by Professor McGonagall (though she does not teach it in My Immortal). It does not necessarily involve the complete transformation of an object, but can also include altering an object's appearance. It can also involve switching traits or parts between two objects, and a host of other possibilities.
Within the category of Transfiguration is the act of Conjuration, in which objects can seem to come out of thin air. Hints of this are seen in My Immortal, such as in Chapter 29 when McGonagall creates chains on Harry, Draco, and Ebony. Ebony likewise casts a "Pop Addelum" spell in Chapter 43, resulting in chains appearing over Loopin. However, Tara doesn't seem to realize Conjuration is part of Transfiguration.
Healing
Perhaps unsurprisingly, the healing arts are barely mentioned at all in My Immortal. The only reference to them is by B'loody Mary, in the chapter written by the anonymous author: B'loody Mary shouts out for "the healers" after Ebony is shot.
Difference from the Original
In the original canon, a healing spell was just a spell that improved the physical condition of a living object. With this skill, one could heal broken bones, clear the throat of someone choking, heal deep gashes, and various other abilities. As goths like to hurt themselves, this would have no place in Tara's warped view of wizardry.
Charms
Charms are never referenced by name in My Immortal, but we do hear of an "Acco" spell, which is used in Chapter 44 by Voldemort to get Navel's wand out of his hand.
Difference from the Original
Charms refer to spells that add certain properties to an object or creature - it differs from Transfiguration in the sense that it changes what an object does rather than what it is. This can include changing its color or having it levitate.
The Charm spell referenced in My Immortal is a Summoning Charm, which is performed by giving the incantation "Accio," followed by whatever object is desired. However, Tara's use of it in the fanfic confuses it with the Disarming Charm, which involves the incantation "Expelliarmus." In the original canon, it was well known (even by Death Eaters) to be Harry Potter's most favorite spell used in combat (however, Harry never once uses it in the fanfic).
Curses
A few are curses used in My Immortal, which can be categorized in the following ways:
Crookshanks
The Crookshanks Curse (also spelled Crosio, Crucious, Crucio and Cruciatus) is one of the worst curses in the wizarding world. Once cast, it will cause the victim to feel immense, torturous pain.
Ebony is the first to cast it in the fanfic, which she does on Voldemort in Chapter 9 (amazingly enough, though she has the Dark Lord in her clutches, she chooses to stop because she "felt bad for him"). She casts it on Snap in Chapter 29 to help Harry in battle, and then again in Chapter 30 to stop Snap from raping Draco. In Chapter 42, Ebony uses it against Britney when she discovers that the dirty prep released Snap and Loopin from Abkhazian.
The only other character to try to use the Crookshanks Curse is Harry, who tries to use it in Chapter 44 against Snap, but hits the flying car instead, causing it to crash.
Difference from the Original
The Crookshanks Curse is based off of the Cruciatus Curse, which was cast by saying "Crucio." The verb form is "cruciate" or "cruciated." The intensity of the curse was usually dependent upon the sadism of the person casting it: Harry Potter himself uses it on one character, but cannot match the wickedness of someone like Voldemort or Bellatrix. The spell cannot necessarily kill you, but prolonged exposure to the pain can lead to severe brain damage. Experienced wizards are able to deflect the spell or strike the caster and hence stop the incantation - although none of the experienced wizards in the My Immortal universe, Voldemort and Snape included, seem capable of doing that.
In the original canon, the Cruciatus Curse had been labeled since the 1700's as one of the three Unforgivable Curses, meaning that it is illegal to perform it on another human being. In My Immortal, characters use it with complete free will, with absolutely no sign of remorse, nor any hint of repercussion.
It is also important to note that "Crookshanks" was actually the orange tabby cat that Hermione adopted in the third book. Unless Voldemort was deathly allergic to cats, tossing a feline at him would probably only serve to tick him off more.
Abra Kedabra
The Abra Kedabra curse (also spelled Abra Kedavra and Allah Kedavra) is a spell that has no real meaning in the fanfic. Harry uses it against Snap and Loopin in Chapter 11 (casting with his "womb"), but nothing happens. Later on, in Chapter 13, Harry and Ebony hear Voldemort casting it, but as to what effect and against whom it is unclear (though, given the linguistic context, it might had been against God Himself). The last time it is seen is at the very end of Chapter 44, where Ebony casts it (presumably) on Voldemort. The fanfic then comes to an abrupt end, so that we never know what happens (one can only assume it killed Voldemort).
Difference from the Original
The Abra Kedabra curse is based on Avada Kedavra, or the "killing curse." It causes instantaneous death upon the victim. Only two people have ever survived it: Harry Potter, and Tom Riddle (later Voldemort). It cannot be blocked by another spell, except in cases where the spells of the caster and his opponent are locked together. Like the Cruciatus Curse, the Killing Curse is considered one of the three Unforgivable Curses. Nonetheless, students in My Immortal use it with ease - even against Hogwarts professors!
"Abra Kedabra" is, of course, a nonsensical phrase said by little kids doing magic shows. "Avada Kedavra," on the other hand, is an Aramaic phrase which means roughly, "Let the thing be destroyed." "Allah Kedabra" would essentially mean (in an acceptable aramaic/arabic mixture) "Let God be destroyed".
Imperius
The Imperius curse locks a person's legs in place, preventing them from moving. It is used by Voldemort against Ebony in Chapter 9 to keep her from escaping.
Difference from the Original
While the word "Imperius" is actually spelled right, a number of problems come from Tara's use of it. For one, the incantation is actually Imperio, not Imperius; Imperius is the name of the actual curse. For another, the Imperius curse was a spell that would place the victim under the total control of the caster, not simply keep their legs from moving; Tara is confusing it with Locomotor Mortis, or the "Leg-Locker curse," which is something entirely different.
Like the Killing Curse and the Cruciatus Curse, the Imperius Curse is one of the three Unforgivable Curses. However, as the only one who uses it is Voldemort, there's no major change from the canon (unlike the other two curses).