Java String to DateTime

You don't need a DateTime object. java.util.Date stores the time too.

int hours = start.getHours(); //returns the hours
int minutes = start.getMinutes(); //returns the minutes
int seconds = start.getSeconds(); //returns the seconds

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As R.J says, these methods are deprecated, so you can use the java.util.Calendar class:

Calendar calendar = Calendar.getInstance();
calendar.setTime(sdf.parse("2013-09-18T20:40:00+0000"));
int hour = calendar.get(Calendar.HOUR); //returns the hour
int minute = calendar.get(Calendar.MINUTE); //returns the minute
int second = calendar.get(Calendar.SECOND); //returns the second

Note: on my end, sdf.parse("2013-09-18T20:40:00+0000") fires a

java.text.ParseException: Unparseable date: "2013-09-18T20:40:00+0000"
    at java.text.DateFormat.parse(DateFormat.java:357)
    at MainClass.main(MainClass.java:16)

You can create Joda DateTime object from the Java Date object, since Java does not have a DateTime class.

DateTime dt = new DateTime(start.getTime());

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Though the Date class of Java holds the time information as well(that's what you need in the first place), I suggest you to use a Calendar instead of the Date class of Java.

Calendar myCal = new GregorianCalendar();
myCal.setTime(date);

Have a look at the Calendar docs for more info on how you can use it more effectively.

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Things have changed and now even Java (Java 8 to be precise), has a LocalDateTime and ZonedDateTime class. For conversions, you can have a look at this SO answer(posting an excerpt from there).

Given: Date date = [some date]

(1) LocalDateTime << Instant<< Date

Instant instant = Instant.ofEpochMilli(date.getTime());
LocalDateTime ldt = LocalDateTime.ofInstant(instant, ZoneOffset.UTC);

(2) Date << Instant << LocalDateTime

Instant instant = ldt.toInstant(ZoneOffset.UTC);
Date date = Date.from(instant);

You can use DateTimeFormatter

DateTimeFormatter format = DateTimeFormat.forPattern("yyyy-MM-dd'T'HH:mm:ss.SSSXXX");
DateTime time = format.parseDateTime("2013-09-18T20:40:00+0000");