Converting many 'if else' statements to a cleaner approach

You could have a Converter interface. Then you could create a class for each Mimetype like:

public interface Converter {

    public void convertToMp3();
    public void convertToOgg();

}

public class MpegConverter implements Converter {

    public void convertToMp3() {
        //Code here
    }

    public void convertToOgg() {
        //Code here
    }

}

You would need a class like this for each converter. Then you could set up a map like this:

Map<String, Converter> mimeTypeMap = new HashMap<String, Converter>();

mimeTypeMap.put("audio/mpeg", new MpegConverter());

Then your convertToMp3 method becomes like this:

Converter converter = mimeTypeMap.get(mimeType);
converter.convertToMp3();

Using this approach you could easily add different converters in the future.

All untested, probably doesn't compile, but you get the idea

If you use pre-JDK7, you may add an enum for all MIME types:

  public static enum MimeTypes {
      MP3, WAV, OGG
  }

  public class Stuff {
      ...
      switch (MimeTypes.valueOf(mimeType)) {
          case MP3: handleMP3(); break;
          case WAV: handleWAV(); break;
          case OGG: handleOGG(); break;
      }
  }

And have a look at the Stack Overflow question Java - Convert String to enum on how to convert Strings to enums.