Essentially all music that was created in civilized countries in this or previous century is copyrighted so that couldn't really be valid.

What music you can use in your level is fairly intuitive - all that J2O wants is that the actions you take be legal. There are three thresholds worth taking into account:

• Uploading a level with the "Music file" field set to a certain value: you can do this with any file you want and it will be legal, because this doesn't yet mean providing the file. If you don't provide the actual file for download though, this is obviously inconvenient and most people won't bother obtaining the music.
• Uploading a level and linking to a music file download on an external site: you can do this if said external site has sufficient rights to spread the music file, e.g. is an official distributor's or the author's page. This is the case with many less known artists, some of whom make all their works available for free download and others only make a few tracks free as a sort of a "demo".
• Uploading a level packed together with the music file: you can only do this if you, personally, have the rights to spread the music file. Because the majority of us are neither musicians nor music distributors, this option is generally limited to products licensed with a free license. One of the most widely used free licenses in music is the Creative Commons license, which, regardless of its exact sub-type, gives users sufficient rights to use the music in a level they upload to J2O as long as you give credits to necessary people in a way specified in the license.

For the record, all of this applies to all file extensions of music and not only the non-module ones such as MP3 and OGG. However, free license module music is generally much easier to find. For example, Mod Archive distributes most music under the Mod Archive Distribution license, which is also sufficient to redistribute the music zipped together with your level.