Goetic Syllables are words of power connected to a scroll you get early in the game as part of one of the many linear quests.
The scroll recharges in-combat at a rate of one half-Syllable per kill, up to a maximum bank of 10 half-Syllables. Syllables are added one at a time at random when you open the scroll in-combat and press the [+] button, up to a maximum bank of 5.
Syllables take one second/fatigue to use and count as an action, which means effects that increase the time it takes to perform an action increase syllable time as well.

There are five possible Goetic Syllables:

-GOR recovers mana by an amount equal to your level multiplied by two.

-KHAN guarantees your next one attack will be a critical hit. Only the first of a multiple-hit attack is guaranteed to be critical, though a sweeping attack will be critical across the board.

-SHEOL heals you by an amount equal to your level multiplied by two.

-XEYN gives all current enemies a -50% hit chance debuff for ten seconds.

-ZUUL deals magical damage to all current enemies as a sweeping attack equal to your level. Can critically hit.

Goetic Words are special effects that are stronger than individual Syllables. Completion of Goetic Words grants the following bonuses in addition to the normal effects of the Syllables used. They must be done in the order displayed, but they don't have to be performed back-to-back if you want to attack or cast something in between using the Syllables. They do not carry over from battle to battle.

GOR-SHEOL : Mana Drain recovers mana equal to your level multiplied by the current number of enemies.

*GOR-XEYN : Mana Dodge recovers mana the next time you dodge. Is not accompanied by a status symbol anywhere, to my knowledge.

*XEYN-SHEOL : Healing Dodge heals you the next time you dodge. Is not accompanied by a status symbol anywhere, to my knowledge.

(^ These two cannot be chained, even though GOR-XEYN and XEYN-SHEOL look like they ought to be a Mana/Healing Dodge. Trying just gives you Mana Dodge and the normal effects of SHEOL.)

ZUUL-KHAN : Bonus Damage adds damage to your next attack equal to your level multiplied by the current number of enemies.

Hope that helps! To find these, I made a list of all possible combinations and ran through them over time. But if I made a mistake, you found another one somehow, or a new version comes up that adds more, let me know!