OMA is the extension for ATRAC3 files, created by Sony for its portable media players. Files with the OMA extension are only readable with Sony technology. Converting MP3s to ATRAC3 (OMA) files is simple using Sony's free SonicStage application. Though it comes bundled with the now-defunct Sony Connect music store, this can be safely ignored.
Download and install the free SonicStage media player application from the link in Resources below. After you install it, you'll have to restart your PC. Because the ATRAC3 format with the OMA extension were created for Sony portable media players, there are no other players authorised to work with OMA files.
Open SonicStage and go to "Options" under the "Tools" menu. Click the "Location to save imported files" tab on the left. In the top panel, select the location on your PC where you'd like your converted OMA files saved. You can safely ignore the lower panel, as the music store it references no longer exists. Click "OK" and exit the Options menu.
Scroll to "Import" in the "File" menu and select "Music File" from the window that pops up. Find the MP3 you wish to convert and click "OK."
Click the "My Library" tab in the blue box near the top of the window. You should now see the MP3 you just imported. Select it.
Go to "Convert Format" in the "Tools" menu. Select the "OpenMG Audio (ATRAC3)" circle in the window that pops up. Leave the bit rate as "132 kbps" for optimal audio quality. For maximum flexibility with your music, deselect the option that says "Add copy protection after completing conversion."
Click "OK" and wait for the green conversion timer to disappear. Your converted OMA file will now be in the location you selected in Step 2.
You may wish to hang on to your original MP3, as the MP3 file format offers more options for future use than the OMA format.
In installation, read the instructions carefully if you wish to avoid making SonicStage your default media player. If you make this mistake, open your normal media player (iTunes, Windows Media Player, etc) and look in "Preferences" or "Options" to learn how to make it your default again.