From Acme:

An Inoue Nawo title that focuses on a man whose job description includes disposing of dead bodies and the stray who blackmails him into sheltering him.

The "Time Loss Phenomenon," causes all living beings on Earth to be temporarily turned into statues. During Time Loss, only certain humans -- "Recievers" -- can remain active, and they witness the terrible reality of what's happening: otherworldly monsters are attempting to breach the human dimension.

First year middle school student Futaba Sorano and her friend are in the middle of a tennis match when all of a sudden a fish-like monster appears out of the sky. At the same time, everyone around Sorano turns into stone, and then are transformed into monsters. While being chased by these monsters, a mysterious boy named Riu appears, and explains that it is up to her, and the other "Receivers", to use their strange new powers to save the earth from these intruders. Sorano and her fellow Receivers' epic battle to save the earth has begun!

Manga about Leonhardt's life within the Sora no Kiseki story.

Saku Ooyagi returns to his old town after seven years and becomes reacquainted with a childhood friend, the ever-boisterous Mihoshi Akeno; but the reunion is far from merry since his last piece of memory between them is of her falling off a tree and him diving to save her. Regardless, Mihoshi focuses her all into improving their tattered relationship and forces Saku to join her astronomy club.

Basically this manga is about an astronomy club, and slapstick school life comedy as Mihoshi changes Saku's life.

Amasawa Miyako, the middle child of 5 siblings, is the only 'normal' one, the others all being very good-looking and very talented at something. She takes care of them at home with cooking, cleaning, etc. because their parents are very busy at work, but she has to deal with both her own insecurities and people's opinions on how she's not like her brothers and sisters. It also doesn't help that she likes her best friend who's in love with her older sister...

Note: Ch1-2 released by Bad Eggs are Volume 2 chapter 2a and b.

Note 2: The 3rd and 4th chapters are the oneshot called: Sora no Mannaka ~Spring Storm~

From StarryHeaven: Miyako loves Seiji, but he doesn’t know. It’s now spring and the cherry blossoms are beginning to bloom. She’s a boring, normal girl amongst an extremely unique family full of popular and hot siblings. If Seiji thinks that her clueless older sister Hijiri is so great, how is she supposed to confess her love to him? Seiji knows Miyako loves someone, so he says that they should keep their distant for a while, when suddenly she confesses to him! His reaction is not good; he leaves Miyako in tears…if she can’t even talk to him normally, how are they supposed to work things out, especially if Seiji is meeting her older sister? *This is actually the 3rd and 4th chapters of the 1st volume.

Sakurai Tomoki is a normal student whose motto is "normal is the best". If there is one thing abnormal, it is that he often dreams of a girl whose face he cannot even remember, and when he wakes up from that dream, he would always be crying. He tried leaving it as just a dream... but one day, from the sky, an angel descended.

The kick-off chapter of the Official Sora no Otoshimono spin-off 4 panel manga. The story revolves around the three Angeloids naming Astrea, Ikaros & Nymph and how they go about their not so ordinary life on earth.

The main characters are Okamoto and Koizumi. Okamoto is an athlete, more preciously a basketball player. He just entered his high school just to be with his girlfriend, Yumi.

There is a backstory between Okamoto and Yumi. Yumi has a large ugly scar on her back. Okamoto accidently dropped a boiling kettle on her back when they were elementary kids. Since then, Yumi threatened Okamoto to be responsible for what he had done by forcing Okamoto to be Yumi's man. Even though it does not clearly show, they regularly have sexual relationships.

All that changes when the short and skinny Koizumi joins the basketball club. Koizumi is generally described as cute and feminine. You cannot even tell whether he is male or female in casual clothing.

From Wingtip Cafe:
After Violet's parents died, a dark-haired philosopher comes to the village and informs her that she is the heir of the "Heaven" clan.

NEETs are people who have chosen not to be part of society due to personal problems or just straight-out laziness.

This story is centered around a certain young woman who has become a NEET right after high school without even realizing it. In her case, though, it's not that she doesn't want work - but rather that there is not a single job out there which can fulfill her very specific criteria...

Oh, well...at least her mother understands her!

1-3
From Elision-Scans:
What does it mean when a sky elf suddenly arrives on our beautiful island?

4-5
Side Stories

On the school rooftop rumored to be haunted by the ghosts of twins, Shuji Yashiro meets Roku Ichinose, a popular boy Shuji always thought of as belonging to a completely different social world. Unable to take his eyes off Roku’s face, Shuji takes his picture on impulse. The following day, while organizing old photos in the clubroom, Shuji finds a shocking photograph that unexpectedly brings his world a little closer to Ichinose's...

Sorako and Sorao met in the school office when they both had transferred to a new school. They became friends really fast, but a short bubbly girl comes and claims she likes Sorao. What will Sorako do? A really nice love story.

Ever since the gate to the Youma world was opened, the Youma have been coming through into our world and wrecking havoc. Luckily, there is a police force specially designed to take care of such a problem. Sora is a newcomer who's stepping in to take over where his brother left off with his Youma partner Arashi. Can the two get along and really become true Youma detectives?

Note: Originally a one-shot-turned-series, it changed names to Omaga Police Sora to Arashi mid-run.

Harasen, a single, lonely 37 years old highschool teacher is unable to cope the departure of a student, who is also his subject of unrequited love. Faced with a love sickness, he returns to the clubbing scene to start afresh where he tangles up with a very troublesome guy...

From Chibi Manga:

Ten and Rio are friends from the old days. they will become high school students starting from this spring, Ten stills carries a certain memory in her heart....?

Contains Sekai wa Kirai de Afureteru

From MangaHelpers:

Shou lives out in the country. He has a big crush on his childhood friend Sora, but is afraid that she thinks of him only as a little brother. One day, Sora announces that she was abducted by aliens. Later that day, Shou confesses his feelings for her and she dies shortly afterward. Shou is still in shock from her loss, when an alien girl named Lila comes down from the sky. She has a disk that contains a brain scan of Sora, and she can run Sora's personality in her own body. She also wants to have a child with him. Will Shou be able to cope with all of these sudden changes, and will he be able to keep Sora with him after all?

Scenery that we have never seen. Sounds that we have never heard. Scent that we have never smelled. Food that we have never tasted. And the surge of emotion that we have never experienced. This is the expedition of recollecting the pieces torn apart and sensation left alone. When we reach that place, what will we think? Howling, 40 degree angle. Raging, 50 degree angle. Shouting, 60 degree angle. A wilderness beyond the heavy sea. The furthest south, far from civilization. At the top of the Earth. We will find lights through the girls' eyes to live tomorrow.

When the Devil King announces his retirement, he calls forth his two sons, Yomi and Sora, to give them each a quest. Whichever of them finds a pure Yamato maiden within a year would inherit the throne of the Devil King, while the other would die. Thus begins Sora's sex-fuelled adventure to find a woman that can satisfy his father...
(Sakigake!! Otokojuku Wiki)