If we call the common height of all these pieces one unit, then collectively they contain 24 cubic units' worth of stuff. So we might expect that they form a cuboidal block of size, let's say, 2x3x4 units. But I think this is impossible!
Let me introduce a bit of notation. Suppose the block we're trying to build is $l\times m\times n$ units in size. Call the things there are $2l\times 2m\times 2n$ of "cubies", the things there are $l\times m\times n$ of "cubelets", and the whole thing the "block". Say that two cubies are "of the same type" when they occupy corresponding spaces in two cubelets. (So there are 8 "types" of cubie in the block, 24 of each type.)
Now, five of those eight pieces are made out of 2x2x2 units, which means that wherever you place any of them in the block they will have equal numbers of cubies of each type. The whole block, of course, also has equal numbers of cubies of each type. So when we place the three remaining pieces -- the ones with parts just one cubie in thickness -- they too must, taken together, have equal numbers of cubies of each type.
Two of those three pieces are the same. Wherever you place one of these, it will contribute 1 cubie of each of four types and 3 of each of the other four types. In particular, it will contribute an odd number of cubies of each type, and between them these two pieces will contribute an even number of cubies of each type.
So, no matter how we place the seven pieces we've considered so far, the number of cubies of each type will have the same parity: all odd, or all even. So we must place the last piece so that it too contributes equal-parity numbers of cubies of each type (since in the completed block we have equal numbers of each type of cubie).
But this can't be done! That piece provides 1 each of two types of cubie, 3 each of two types of cubie, and 2 each of the other four types of cubie. (Exactly which types are which depends on where and how you place the piece.)
So, I think at least one of the following things has to be true.
- The shape these pieces are meant to go together to make isn't a block whose sides are all integer multiples of one "unit" with no gaps.
- They go together in some super-weird fashion where they are at non-right angles or non-"integer" positions or something. (This seems obviously impossible, but maybe my intuition is broken.)
- They aren't actually the right set of pieces; there are some more, or some of these are from a different puzzle and just happen to look like they're the right size for this one, or something.
- The puzzle is some sort of a hoax or trick, impossible by design.
- There is some boneheaded mistake in my analysis above.
One kinda-plausible possibility is that they form a 3x3x3 cube with some gaps (and part of the challenge will presumably be to assemble things in the right order, which will need some burr-puzzle-style sliding around). Another, mentioned by Jaap Scherphuis in comments, is that these are actually pieces from two separate puzzles (probably made by the same people since the pieces are so similar).