Note: Starting from OpenMPT 1.27, this workaround is no longer required. All standard DMOs are emulated right within OpenMPT without the need to install anything.
This has been asked a couple of times (not necessarily on this forum), so I thought I should probably write this down in a place where people can find it. So here goes:
It's really simple. Run winetricks dsdmo, restart OpenMPT, and you're done! Now your modules with DMO effects will sound just the same as they did on Windows.
Caveat: This currently only works with the 32-bit version of OpenMPT. If you have access to a 64-bit Windows machine, you may able to obtain a 64-bit copy of dsdmo.dll from that machine for the 64-bit version of OpenMPT, though.