Psycho Staff

Psycho Staff is a completed 2007 Comedy Science Fiction Seinen manga by Mizukami Satoshi, the creator of The Lucifer and Biscuit Hammer and Sengoku Youko, among others.

Ordinary High School Student Hiiragi recieves a love note one day, saying: "To Hiiragi Kouichi-kun. I'll be waiting for you after school behind the school gym. Sakuragi Umeko." Having never gotten a love note before, he is surprised and complies. There he meets Sakuragi, a strange girl asking him to come to the planet R'lyeh. Hiiragi is disappointed that his first admirer was a nutcase, and leaves. When he gets home, there's Sakuragi, asking him to come again. Hiiragi is doubtful, but then again, could the planet be real? The girl is strange and he's pretty strange himself...

Not to be confused with Psychostick.

Tropes used in Psycho Staff include:

Agent Scully: Hiiragi. He absolutely refuses to believe in the aliens at first.
Brought Down to Normal: Hiigari after the meteor is stopped.
Call to Adventure: "I came here to recruit you into 'Space Esper Corps' of the planet R'lyeh!"
Death From Above: The meteor that threatens to turn the town into a crater.
Freud Was Right: Hiiragi's attraction to Himehagi-sensei is based upon her resemblance to his deceased mother. Which was her plan all along, when she chose her disguise to hide amongst humans, making this an Invoked Trope.
Genki Girl: Sakuragi, though subverted. She's a soldier.
Girlish Pigtails: Worn by Sakuragi
Hard Work Hardly Works: Argued and averted. Sakuragi has a huge complex about the value of her hard-won skills compared to Hiiragi's incredible native talent. Hiiragi thinks her dedication and skills are amazing, and that his psychic powers are a fluke and ultimately useless in real life. At the end, when Hiiragi's powers disappear, it's a damn good thing for him that he had felt this way, or he'd have no life skills or prospects now that he has to be normal.
Human Aliens: Sakuragi and Himehagi-sensei.
Humble Hero: Hiigari. His father even mentions it at the end of the series.
I Just Want to Be Normal
Manic Pixie Dream Girl: Sakuragi. Subverted fast, and Hiiragi wants nothing to do with her manic-pixie-dream offerings anyway.
Missing Mom: Hiiragi's mother died years before.
My Eyes Are Up Here: Himehagi-sensei to Sakuragi, here.
Lethal Chef: Sakuragi. Which makes perfect sense as she's an alien and probably doesn't know how to cook Japanese food.
Long-Distance Relationship: Incredibly long distance between Sakuragi and Hiiragi.
Only Six Faces: Justified as there are only about six characters.
Ordinary High School Student: Hiiragi
Panty Shots: Often from Sakuragi.
Power Incontinence: Hiiragi has a hard time controlling his powers at first.
Psychic Powers: Hiiragi has ESP.
Random Power Ranking: Hiiragi is a one-in-five-billion B-class psychic who has a temporary upgrade to A-class later on. Avoids the problems of Rank Inflation because the series is so short and Hiiragi is the only psychic that shows up.
Refusal of the Call: Hiiragi doesn't believe her the first time.
Robot Buddy: Sumeragi's size-changing robot companion, Transit. Small enough to hide in a backpack when need be, but can grow to the size of a small building.
Scaramanga Special: Sakuragi can project a wormhole out of a gun.
Shout-Out: Mostly to the Cthulhu Mythos. Sakuragi's homeworld is named R'lyeh, and their currency is called "dagon." The people of R'lyeh are also at war with the people of Yaddith.
Strange Girl: Sakuragi
Slap Slap Kiss: Sakuragi kicks Hiigari just after he declares his love for her. She kisses him a moment later.
The Resenter: Hiiragi. He'd rather study to get into university than be an intergalactic hero.
Title Drop: The ESPer corps back on Sakuragi's homeworld is sometimes called the "Psycho Staff," which is in emulation of a previous group of long-gone A-class psychics who made up the original Psycho Staff.
Unlucky Everydude: Hiiragi
What Measure Is a Non Super: Subverted and averted. Hiiragi would rather be normal and go to college than use his amazing powers in war -- or much at all. Sakuragi, meanwhile, is hard-working and dedicated, traits which draw Hiiragi's admiration and which save them when "Sensei" outmatches Hiiragi with a suit that replicates psychic powers.
You Gotta Have Blue Hair: The mangaka's notes at the end of chapter 6 point out that Hiiragi (and all psychics, actually) have green hair, though he wasn't able to work it into the narrative. His green hair is visible on the collection's cover, though.
Zettai Ryouiki: Sakuragi's outfit.