DateTime("2019-08-07T19:20-5:00") conversion to local date time with offset value

You cannot use an ISO formatter if you don't get an ISO String… The problem seems to be the format of the offset you get, it is +H:mm instead of the one used in the ISO standard, that is +HH:mm. In words: It does not consider single-digit hours.

You will have to build a specific DateTimeFormatter for this situation.

Unfortunately, Java 8 does not support patterns with a single-digit representation of offset hours, but if you can use Java 9 or higher, you'll be able to define a DateTimeFormatter that considers zone offsets formatted as +H:mm:

Java 9+

public static void main(String[] args) {
    DateTimeFormatter dtf = new DateTimeFormatterBuilder()
                                    .append(DateTimeFormatter.ISO_LOCAL_DATE_TIME)
                                    .appendOffset("+H:mm", "UTC")
                                    .toFormatter(Locale.ENGLISH);
    OffsetDateTime sourceDateTime = OffsetDateTime.parse("2019-08-07T19:20-5:00", dtf);
    System.out.println(sourceDateTime.getOffset());
}

This uses the ISO formatter for a LocalDateTime and appends a specific pattern for parsing offsets.

Admittedly, I'm not sure if "UTC" is a good (hard-coded) choice as a default offset in case the String does not contain any.

Output of this code:

-05:00

Java 8 --> String manipulation

public static void main(String[] args) {
    // provide some variants of input
    List<String> variants = List.of(
            "2019-08-07T19:20-5:00", "2019-08-07T19:20+5:00",
            "2019-08-07T19:20-05:00", "2019-08-07T19:20+05:00"
    );
    
    // handle offset extraction via String manipulation for each variant
    variants.forEach(variant -> {
        String parseable = variant;
        /*
         * This assumes an offset always has a sign and 
         * a colon that separates hours and minutes.
         *
         * Get all their indexes in order to find the offset
         */
        int lastIndexOfColon = variant.lastIndexOf(':');
        int lastIndexOfMinus = variant.lastIndexOf('-');
        int lastIndexOfPlus = variant.lastIndexOf('+');
        
        /*
         * Decide which sign actually leads the offset
         * (it's either a plus or the very last minus).
         * In either case insert a leading zero if the amount of digits/chars
         * between '-'/'+' and ':' is 1, otherwise don't do anything…
         */
        if (lastIndexOfMinus > lastIndexOfPlus && lastIndexOfMinus + 2 == lastIndexOfColon) {
            parseable = variant.substring(0, lastIndexOfMinus + 1) 
                        + '0' 
                        + variant.substring(lastIndexOfMinus + 1);
        } else if (lastIndexOfPlus + 2 == lastIndexOfColon) {
            parseable = variant.substring(0, lastIndexOfPlus + 1)
                        + '0'
                        + variant.substring(lastIndexOfPlus + 1);   
        }
        // then parse the manipulated String
        OffsetDateTime odt = OffsetDateTime.parse(parseable);
        // get the offset
        ZoneOffset zoneOffset = odt.getOffset();
        // and print some result
        String msg = String.format("%s has an offset of %s", variant, zoneOffset);
        System.out.println(msg);
    });
}

The output of this example is

2019-08-07T19:20-5:00 has an offset of -05:00
2019-08-07T19:20+5:00 has an offset of +05:00
2019-08-07T19:20-05:00 has an offset of -05:00
2019-08-07T19:20+05:00 has an offset of +05:00

Another way could be to separate the offset part from the date and time and create a ZoneOffset.of(int, int) using parsed values left and right to the last colon. Parsing the date-time part and applying the offset afterwards could also lead to the desired result.

This is the correct code

OffsetDateTime sourceDateTime = OffsetDateTime.parse("2019-08-07T19:20-05:00");
System.out.println(sourceDateTime.getOffset());