If you've never played the game with these settings enabled, you are in for a treat. I have personally tested and confirmed this fix works in patches 1.05b, 1.07, and 1.09b. However, to my knowledge, this was a day 1 feature, and should work with all versions of the game.
Here are the steps you will need to follow:
1. Download the following attachment (compressed with 7zip)
2. Extract the compressed folder into the directory of your choosing, and then move the two DLL's into your Diablo II folder.
3. Launch Diablo II, press ESC, click Options, choose Sound Options, and then click the options for 3D Sound and Environmental Effects. The files you added should allow you to toggle these settings to "ON" (as shown in my screenshots below).
3D sound

EAX

In case you'd like to read more, I have added the source below. Also, note this works with several other games as well, including Blizzard titles, such as Warcraft 3!: