A semi-side quest that is ominously prophetic, given the game in which it appears, HANGMAN shows up pretty early in OMORI. During your third trip to WHITE SPACE you'll need to check the laptop, and when you do you'll be taken to the HANGMAN page, which you can thereafter access anywhere by hitting a button / key (which changes based on your system).
Each letter of the alphabet is displayed on this screen, and each comes paired with a clue that vaguely describes a specific location. If you go to that location you'll find a letter. Pick it up with OMORI - anyone else is leading the party the letter will be blurred out - and the key will be added to the HANGMAN page. The letters often leave behind cracks in the ground, as well, which are worth checking for hints as to the overarching plot of OMORI.
The SUNNY ROUTE will allow you to collect 23 of the 26 letters of the alphabet. Among them are the answers to the HANGMAN puzzle, which create a sentence that ultimately guides you to one of the final areas of the game. You will be forced to collect these keys. The rest of the letters - including the three you can't collect on the SUNNY ROUTE - are important to an optional dungeon in the OMORI ROUTE, where you can gather all 26 on your journey.
This guide will help you track down the 26 keys of the HANGMAN side quest. Note that only OMORI can pick up the keys, so if you see a black object that's obscured by a blur, TAG in OMORI and let him pick up the key.
A
The first key you'll come across is the A key. It's located just south of the stump where you begin all of the HEADSPACE segments. It will appear during your second trip to HEADSPACE, during the PROLOGUE. This letter is necessary for completing the SUNNY ROUTE.
B
Next up is the B key. You'll find it on FOGGY BRIDGE, which spans the two sections of VAST FOREST. This letter is necessary for completing the SUNNY ROUTE.
C
Third, of course, is the C key. It's located in PINWHEEL FOREST, up the ladder in the eastern half of VAST FOREST. You'll gain access to PINWHEEL FOREST once you've completed the JUNKYARD in OTHERWORLD, though you'll need to make the trip all the way back down the ladder. Easier to just wait until THREE DAYS LEFT. This letter is necessary for completing the SUNNY ROUTE.
D
Fourth - though more likely to be the third - is the D key. It's in the JUNKYARD, on the largest heap of traversable garbage you can find, the one where you can sit on a couch and watch the moon when you reach the top. Check the west side of the upper level to find the key, sitting outside.
E
Enough counting. Next up is the E key. This is one of the obligatory keys for the SUNNY ROUTE, and it'll appear on CAPT. SPACEBOY'S bed after you defeat him. This letter is necessary for completing the SUNNY ROUTE.
F
The F key shows up shortly after the E key. You'll find it inside the barn in CATTAIL FIELD, just moments before the end of the PROLOGUE. You can't miss it.
G
The G is in FROZEN LAKE in OTHERWORLD, though you can only reach it while playing the OMORI ROUTE. Once you've reached ONE DAY LEFT and can explore HEADSPACE with impunity, head to OTHERWORLD CAMPSITE and speak to PINKBEARD in the SPACE PIRATE SHIP. You'll receive BATTERIES, as well as a quest to find his son, CAPT. SPACEBOY.
Head to FROZEN LAKE. Inside the igloo you'll find a fish on the wall. Put the BATTERIES into the fish and it will begin to sing a song. Let it play the entire song and the trap door in the igloo will swing open. Beneath it you'll find a teleporter to SNOWGLOBE MOUNTAIN, and on the other side of the teleporter you'll find the G key.
H
The H key is hidden deep within the LOST FOREST, a subsection of PYREFLY FOREST. To find this secretive area you need to make your way to the end of the train tracks, where the track is obstructed by debris. Poke through the woods to the southeast of the tracks to find a maze protected by cat-spider hybrids. Light candles to get them out of your way and proceed to the far east side of the area, where you'll see SOMETHING.
Keep following the path until you reach a dead end, along with an item. A STRANGER will disappear into the forest behind the item. Check the trees to enter the LOST FOREST, a misty, darkened spot inhabited by the talkative DADDY LONGLEGS. To make your way through this area you need to only go down the paths guarded by GHOST BUNNIES. At the end of the LOST FOREST you'll find DADDY LONGLEGS one last time, and when he vanishes you'll find the H key.
I
The I key is in THE DUNGEON of SWEETHEART'S CASTLE, inside one of the southeastern cells. To reach it you'll need to go through the tunnels beneath THE DUNGEON, hitting switches until you reach the cell next door. The switch inside this cell with open the cell with the I key.
J
The J key is found amongst the cluster rooms behind the ROYAL KITCHEN in SWEETHEART'S CASTLE. Head north down the central hallway and you'll see it inside a cage. Use AUBREY to smash it open, then switch back to OMORI.
K
The K key is in SWEETHEART'S CASTLE. You'll find it in the ROYAL GALLERY, located in the southwestern wing of the castle. It's the first side area you'll come across in this wing, past the lines of running SPROUT MOLES. This letter is necessary for completing the SUNNY ROUTE.
L
The L key is in the LOST LIBRARY, beneath the theater that is the 'front' of SWEETHEART'S CASTLE. You'll be forced to go through this area once you've defeated SWEETHEART, and finding the L key will allow you to leave. This letter is necessary for completing the SUNNY ROUTE.
M
The M key is at the bottom of the DEEP WELL. You'll come across it on your first trip to the LAST RESORT. This letter is necessary for completing the SUNNY ROUTE.
N
The N key is on the bottom floor of LAST RESORT. You'll find it by one of the card tables on the west side of the room.
O
The O key is located in GHOST PARTY, sitting near the tables with all the Os. You can access GHOST PARTY via the haunted pool that's to the right of the entrance of the LAST RESORT. This letter is necessary for completing the SUNNY ROUTE.
P
The P key is in LAST RESORT. You'll find a bathroom on the ground floor of the casino, near the stairs in the north. The key is sitting in the open stall. (Get it? P key? Bathroom? Badum-tsst.) This letter is necessary for completing the SUNNY ROUTE.
Q
The Q key is, yet again, in LAST RESORT. You'll find it in the elevator on the fifth floor, behind BERLY. Get her a BOTTLED WATER and she'll let you onto the elevator.
R
The R key is on FOGGY BRIDGE in VAST FOREST, and you can see it early in OMORI, but you can't actually get to it until you reach LAST RESORT. Head to the fourth floor of LAST RESORT once you've reassembled the party. In the right room you'll find a hole out to a construction site. To climb it properly you'll need AUBREY to bash barrels out of your way. The R key is at the very top of the tallest ladder, which pokes out of the water and up to an island in FOGGY BRIDGE.
S
The S key is at the west end of UNDERWATER HIGHWAY. If you're traveling along the highway itself you'll find it just after the third TOLL GATOR booth. If you take the back route to avoid the TOLL GATORS you'll find it by heading back east from the end of the road, just south of one of MARI'S picnic blankets. This letter is necessary for completing the SUNNY ROUTE.
T
The T key is located in DEEPER WELL. You need to defeat HUMPHREY to get at it, however, so you'll need to trek through the entirety of the whale's guts. Once you're shot out of HUMPHREY the T key will be sitting nearby. This letter is necessary for completing the SUNNY ROUTE.
U
The U key is located in HUMPHREY, down the eastern path. Take the left path twice when you hit the rapids near the end of this wing of the whale's innards to find the key.
V
The V key is found within HUMPHREY, down the western path with the three colored puzzles. Enter the green puzzle and you'll find a cage just north of the first conveyor belt. Bash it open with AUBREY and the V key will be inside.
W
The T key is sitting in DEEPER WELL. When you defeat HUMPHREY and get shot out it'll be sitting right beside the T key. This letter is necessary for completing the SUNNY ROUTE.
X
The X key is on the third floor of DINO'S DIG in ORANGE OASIS. You'll find it under a bread-shaped heap of ground in the bottom-right corner of the area. This is the most dangerous floor of DINO'S DIG, so you'll probably need to have your level in at least the low 30s to get this high.
Y
The Y key is in the snow field just before you reach SNOWGLOBE MOUNTAIN, making it another OMORI ROUTE-exclusive. Zig-zag towards the northeast corner of the map. (And if you don't find it before you reach the corner, zig-zag back to the southwest. The chances of accidentally walking past it are much smaller if you're working from the outside in.)
Z
The Z key, fittingly the last you're likely to find, is only available on the OMORI ROUTE. You'll find it during your explorations of HEADSPACE on ONE DAY LEFT by heading all the way west along UNDERWATER HIGHWAY. Just before the road ends you'll find a HITCHHIKER who will offer to take you to THE ABYSS, the place where the HANGMAN keys get put to work. The Z key is right at the entrance of THE ABYSS.
Fittingly, the Z key is right in the spot where you need the rest of the keys. Once you've acquired all 26 HANGMAN keys the game will crash (might depend on your system), and when you open it again you'll be right where you were. Once this happens you can approach the dead end of THE ABYSS and open up the rest of the dungeon.