OBVIOUS SPOILER WARNING!

So, after some extensive searching, and then giving up and loading the levels up in the HPL Level Editor, I've finally found all the Strange Artefact locations in the game!
Good hunting!

01 – Level 05: Sewers
In the Sewers, (the area after you have to input the first keypad code in the game) right after you enter a Tuurngait zombie will follow you into the area. Take an immediate left, and then left again and use the valve on the wall to raise the bars. The statue is under the pipe here, next to the locked door.

02 – Level 09: Archives
In the same area as the criss-crossed laser over the moveable bookshelves is a small Museum-like area. It's in one of the display cases, along with a few other artefacts. In order to be able to get to the item, you first need to open up those glass cases. To do this, look at the door you walked in through and on the left (from inside the room) in the corner is a REALLY hard-to-see button made out of the little lion-face on the wall. (Note: I've read that the buttons location could be randomised, so if it's not here, check around the room for it. It should always be one of the lion-face parts though.) When you push it, you’ll then be able to lift up the glass and get to the artefact. However, grabbing it will active the security in the room. Thankfully there’s a way to turn it off too. At the back of the room, opposite the way in, are two bookshelves. Each one has a loose book that you can pull out. The left one is higher up, and the right one is lower down. One you’ve pulled them both out, the alarm will turn off and the door will open!
(BIG thanks to ‘j0j0’ for showing me how to make this glass cases lifetable in this room, which was the key to solving the whole thing!)

03 - Level 11: Not Complete Complex
After turning the power on and entering the huge cave area, you'll enter a series of corridors where you need to use the Gas mask, and there's a creature roaming around. After sliding open the door (that you have to do manually), go left, and then right so you can see the door with a red light above it in front of you. Go to that door and turn right. Ahead of you will be a destroyed section of floor. Just before the hole in the floor, near the ceiling is a vent that juts out of the wall. The Artefact is on top of that.

04 – Level 12: Requiem Residential
After your first trip into 'the past' the next area looks like Area 2 from Requiem. In the upper room that has water on the floor, there's a half-open door into a little alcove above the pipes. Use a box to jump up and grab the statue.

05 – Level 16: Rooms
After leaving the Mess Hall (from Black Plague), enter the door straight ahead down the corridor. You'll have to remove the stuff blocking the door to get through. This will return you to the large set of corridors also from Black Plague. Return to the central area and there will be 4 doors there. You can use the Steel Rod in your inventory to open them up. One of them is destroyed and you won't be able to enter, but go through the door on the same side to enter a room with water on the floor. The Artefact is in the sink in the bathroom

06 – Level 17: Complex
After a long corridor with deactivated lasers (that you deactivated yourself using the computer), there's a warehouse room with a large fan on one wall. Here, there are two entrances into the vent system; one at the back of the room and one in another room to the side. Using either one, you'll be heading in the same direction, then go right, all follow the path straight to the end of the vent. You'll pass an opening in the vent to your left and eventually find a grate on the floor that you can open with your Vent Tool. Do so and drop down into the room and you can find the statue behind the black boxes in the corner.

07 – Level 19: Outside Hangars
Once you get to the outside surface area, you'll have to enter two large hangers to find Gasoline. In the one where you need to ride the box over a locked gate is a darkened room at the back of the hanger. Use a box in climb inside this dark room and you can find the Artefact on the vent near the ceiling.

08 – Level 22: Old Mine Storage
Once you fall into the mines, you'll eventually reach a small storage area full of several rooms and a trapdoor into the spider-infested basement. In the back room of this area with a jammed door and the Ladders, the statue is on a high shelf immediately left are you walk in through the door.

09 – Level 26: Iron Mine Rails
Once you've gone past the flames and have turned the valve to open the door, You'll be in a series of corridors with a Tuurngait zombie wandering around. Turn right, and keep following the the right wall all the way around until you see some boxes in a dead end. The Artifact is in the open one.

10 – Level 28: Temple Cellar
At the very far end of the area, after doing the crawling around underwater you reach a room with a Sphere on a pair on hands. On either side of this room is a little alcove with a dead tree inside it. The statue is hidden in the one of the left (from walking into the room)