If your DER files are in PKCS#8 format, you can use the Java KeyFactory and do something like this:

// Read file to a byte array.
String privateKeyFileName = "C:\\myPrivateKey.der";   
Path path = Paths.get(privateKeyFileName);
byte[] privKeyByteArray = Files.readAllBytes(path);

PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(privKeyByteArray);

KeyFactory keyFactory = KeyFactory.getInstance("RSA");

PrivateKey myPrivKey = keyFactory.generatePrivate(keySpec);

System.out.println("Algorithm: " + myPrivKey.getAlgorithm());

You mentioned that you may not know what algorithm the key is using. I'm sure there is a more elegant solution than this, but you could create several KeyFactory objects (one for each possible algorithm) and try to generatePrivate() on each one until you do not get an InvalidKeySpecException.