Not so long ago I was looking for a comprehensive list of openings (and received an excellent answer with a huge list). Hearing a lot about unsound openings, I am curious whether I can have a comprehensive list (I have read this answer, but it is just a few gambits) of unsound openings.
This is not an answer, just an explanation why it is difficult to generate a list of unsound openings.
There is the famous quote "Any opening is good enough to be played if its reputation is bad enough" - Tartakower. This tongue-in-cheek quote implies that there are many good ideas in openings which are considered refuted or unsound. More specifically, "If an opening cannot be refuted by concrete variations, it is playable, even when it appears on the verge of catastrophe" - Averbakh. So, for an opening to be considered unsound, it has to fail to some specific tactic.
Lets highlight this with a game. The game below is a mismatch between Karpov (elo 2725) against Miles (elo approx. 2575). Miles plays the eccentric St George variation, 1. e4 a6 and wins! Miles chose this opening because he knew Karpov had an encyclopedic knowledge of all the mainstream openings.
[White "Karpov"] [Black "Miles"] [FEN ""] 1. e4 a6 2. d4 b5 3. Nf3 Bb7 4. Bd3 Nf6 5. Qe2 e6 6. a4 c5 7. dxc5 Bxc5 8. Nbd2 b4 9. e5 Nd5 10. Ne4 Be7 11. O-O Nc6 12. Bd2 Qc7 13. c4 bxc3 14. Nxc3 Nxc3 15. Bxc3 Nb4 16. Bxb4 Bxb4 17. Rac1 Qb6 18. Be4 O-O 19. Ng5 h6 20. Bh7+ Kh8 21. Bb1 Be7 22. Ne4 Rac8 23. Qd3 Rxc1 24. Rxc1 Qxb2 25. Re1 Qxe5 26. Qxd7 Bb4 27. Re3 Qd5 28. Qxd5 Bxd5 29. Nc3 Rc8 30. Ne2 g5 31. h4 Kg7 32. hxg5 hxg5 33. Bd3 a5 34. Rg3 Kf6 35. Rg4 Bd6 36. Kf1 Be5 37. Ke1 Rh8 38. f4 gxf4 39. Nxf4 Bc6 40. Ne2 Rh1+ 41. Kd2 Rh2 42. g3 Bf3 43. Rg8 Rg2 44. Ke1 Bxe2 45. Bxe2 Rxg3 46. Ra8 Bc7 0-1
To answer your question, you would need to figure out which openings have a concrete tactical refutation, rather than ones that are offbeat.