Mieu is a small blue mammalian called a cheagle. Cheagles are considered sacred by the Order of Lorelei due to a pact formed with Yulia Jue, symbolized by the Sorcerer's Ring. The ring enables cheagles to communicate with others, as well as use the power of various fonons to gain new skills.

He joins Luke's group when the elder cheagle exiles him for setting fire to the forest where ligers live, which causes the ligers to hunt the cheagles for food. Since Luke saved Mieu's life, the elder orders him to serve Luke for the time of one year.

Source:Wikipedia

Emiri is a soft-spoken, well-groomed second-year student with long, light green hair and first appeared in "Mystérique Sign", seeking counsel from the SOS Brigade.

Emiri later reappears as the secretary to the president of the Student Council.
By this time, it is implied that she is Yuki's superior, or at the very least her minder. Emiri is also later shown to work part-time (against the rules of the School Council ) as a waitress in the cafe frequented by the SOS Brigade.

Source:Wikipedia

Tsuruya is the hyperactive friend of Mikuru (from the current time plane), notable for her loud voice, knee-length hair and prominent tooth, who possesses a cheerful and friendly disposition. Her fang-like tooth gives her an idiosyncratic speech pattern, causing her to misspeak words by leaving out syllables. Her speech pattern is often accompanied with a lisp and catch phrases of "megas" and "nyoro". She was also named "honorary consultant of the SOS Brigade" by Haruhi.

She appears relatively sparingly throughout the anime.

Source:Wikipedia

Mikuru is a time traveler. She is assigned from the future to investigate the reason for the inability to travel to any point in time before three years prior to the present story.

She is very shy and timid and unfortunately, the odd end out of many a Haruhi eccentricity. Whenever she speaks of her mission or of her time plane, she inserts the word 'classified' into spots that would ordinarily reveal important information.
In the English version, she answers all of Kyon's probing questions with 'That's classified'.
Occasionally, Mikuru's older self will appear in the same time plane, essentially threatening a time paradox should anyone other than Kyon find out, meaning these visitations are exceedingly rare and unpredictable.

Source:Wikipedia

Koizumi is an esper. He suddenly acquired the knowledge and powers of an esper three years prior to the present story. Along with other espers, he uses his power to combat beings of energy within Closed Spaces created by Haruhi during times of fitful irritation at the lack of strange phenomena in her world. Like with the other members, his so-called Agency and its members are never explored in-depth.

Source:Wikipedia

Kyon is the narrator and the main protagonist of the series. He is a student, with whom Haruhi willingly interacted. Even though Haruhi is the title character, the story is told through his viewpoint. Through narration and dialogue, he provides his insight, perspective, and opinions on the series' events.
While Kyon's intentions toward defending his Brigade fellows from Haruhi's madness are often well intentioned, he often has to struggle to overcome the crazy and often ridiculous obstacles barring his way. While he's not afraid to stand up to a Haruhi tangent, he does exhibit a form of fear over her occasional troublesome antics that could threaten expulsion or worse.

Kyon is, in fact, a nickname. Kyon's real name has yet to be revealed.

Source:Wikipedia

Haruhi Suzumiya is the title character and leader of the SOS Brigade , whose energetic and eccentric character proves to be the driving force for the series. She has a mind for adventure which often leads her subordinates to be swept into her plans. Haruhi cannot stand boredom so she comes up with various activities for the SOS Brigade, making them participate whether they like it or not.

While being smart, beautiful and energetic, Haruhi was eyed as an oddball ever since middle school. What Haruhi does not know is that she has an outstanding power to change the environment around her as she pleases, and by subconsciously using it she gathers Mikuru Asahina, Itsuki Koizumi, and Yuki Nagato into one place, the SOS Brigade.

Source:Wikipedia

Her full name is Mystearica Aura Fende. She is 16 and is a Locrian Sergeant of the Order of Lorelei in the Intelligence Division. She is extremely disciplined and feels compelled to be a soldier at all times. She is also a descendant of Yulia and can sing Yulia's Fonic Hymns. She also has a secret fondness for cute things.

Source:Wikipedia

Jade, formerly known as Dr. Jade Balfour, is a colonel of the Malkuth Empire.
He is sarcastic, pessimistic, honest and logical. He is known as the "Necromancer" for having animated the corpses of dead men and is the creator of fomicry, a field of science as a means of creating replicas. Jade is also very knowledgeable about the fonic artes.

Source:Wikipedia

Guy is a swordsman in service to the House of Fabre. He is 21 and is very loyal and affectionate towards Luke. It is revealed that due to a bad experience during his childhood, he is morbidly afraid of any physical contact with women. It is also later revealed that he was originally from Hod and that his real name is Gailardia Galan Gardios.

Source:Wikipedia