The Stained Soil locations quest is the first thing that truly stumped me in Midnight Suns. It's not exactly an Easter Egg hunt: you're looking for evidence of the remains of witches killed by Hiram Shaw, the cruel Reverend of Salem in the Marvel universe.
Had I unlocked enough of the Abbey locations to be able to locate the Stained Soil samples? Did I need to complete the Standing Stones puzzle? Midnight Suns doesn't give a ton of direction.
The good news: if you're struggling with it, there's no hurry to complete the quest. The Abbey stuff, for the most part, runs independently from the campaign, and I was able to do a bunch of story missions even though I hadn't made progress on finding the Stained Soil. If you need help, though, here's a step-by-step walkthrough.
Search The Study
Right before you start the Stained Soil quest, Midnight Suns asks you to "Search the Study" in Shaw's Church, a centuries-old building on the east side of the map. Agatha keeps going on about "There must be something we're missing." Not very helpful, ghost grandma!
Turns out, you have to cast the second Word of Power, "Atum," at the desk in the middle of the room, where a magnifying glass overlooks an otherwise empty table. The first clues ("Coven Suspects," as sketched contemporaneously by Shaw), about the location of the Stained Soil are revealed once you do this.
Find Stained Soil A, B, and C
The same photographs you found in Shaw's Church are magically transported to the library room of the Abbey, adjacent to the Mirror Table. You can revisit them there to put the image fresh in your mind, or find the solutions below.
Stained Soil A location
Fast travel or jog over to the Standing Stones. While standing on the stone monument surrounded by large vertical totems, look north to find a cave in the distance (you can use the map to orient north by looking at the Hunter's icon), down the hill from the Standing Stones.
Shaw's sketch, I eventually figured out, was not of the more prominent cave to the east. This one was the hardest to locate for me.
Stained Soil B location
Southeast of Dreamer's Descent, down the road segment extending from that area you'll find a stone cave. The soil will be beside a table stacked with books.
Stained Soil C location
Follow the river outside the Training Yard until you find the horseshoe symbol stamped to another wooden post on the right side of the river, which terminates beside a cliffwall that's been converted into a little camp, not unlike the other locations.
Find the Hanging Tree
After you deliver all three soil samples at once to Agatha in the library, she'll whisk you down to Agatha's Altar to reveal another sketch, this one depicting another morbid location: the Hanging Tree!
The Hanging Tree is west of Shaw's Church and southwest of Agatha's Cottage. Look for the circle-shaped road on the map in that region. The tree is covered in green glowing runes—it's hard to miss once you stumble on it.