It is going to depend on if they are saved to the phone only, are within the app itself, only accessible by said app (due to the way downloaded or that it is actually linked to files online), etc.
The simplest way is to download move them all to an empty folder on a computer. Then you can organize them how you want, put them in sub folders, etc., and then once all organized the way you want you can then copy or move (I suggest copy so you leave a backup on the computer) them over to the phone by connecting the phone to the computer via USB cord.
You can also save them to the phone's SD card rather than the phone's "Internal" storage, should you chose to.
Once on the phone (or on the SD card), then you should be able to access them through any music app.
Just make sure, before you start it all, that you have the needed room on the phone. If the phone doesn't have enough space (or the card doesn't) then you will have to clear off space to make room for them, or limit the files you put on the phone/card.