Converting timedate timezones with Joda-Time
First of all, currently it does not compile. You should fix that, non-working codes are off-topic here.
According to the Code Conventions for the Java Programming Language, method names should start with lowercase letters and class names should start with uppercase letters. ConvertTimeZones should be convertTimeZones.


Code Conventions for the Java Programming Language, 9 - Naming Conventions
Effective Java, 2nd edition, Item 56: Adhere to generally accepted naming conventions

The o prefix is unnecessary for every variable.
You could omit lots of intermediate objects. Here is a simplified version:

public static String convertTimeZones(final String fromTimeZoneString, 
        final String toTimeZoneString, final String fromDateTime) {
    final DateTimeZone fromTimeZone = DateTimeZone.forID(fromTimeZoneString);
    final DateTimeZone toTimeZone = DateTimeZone.forID(toTimeZoneString);
    final DateTime dateTime = new DateTime(fromDateTime, fromTimeZone);

    final DateTimeFormatter outputFormatter 
        = DateTimeFormat.forPattern("yyyy-MM-dd H:mm:ss").withZone(toTimeZone);
    return outputFormatter.print(dateTime);
}

Here are a few unit tests:

import static ...TimeZoneConverter.convertTimeZones;
import static org.junit.Assert.assertEquals;

import java.util.Arrays;
import java.util.Collection;

import org.junit.Test;
import org.junit.runner.RunWith;
import org.junit.runners.Parameterized;
import org.junit.runners.Parameterized.Parameters;

@RunWith(value = Parameterized.class)
public class TimeZoneConverterTest {

    private final String expectedDatetime;
    private final String fromTimezone;
    private final String toTimezone;
    private final String inputDatetime;

    public TimeZoneConverterTest(final String expectedDatetime, 
            final String fromTimezone, final String toTimezone,
            final String inputDatetime) {
        this.expectedDatetime = expectedDatetime;
        this.fromTimezone = fromTimezone;
        this.toTimezone = toTimezone;
        this.inputDatetime = inputDatetime;
    }

    @Parameters
    public static Collection&lt;Object[]&gt; data() {
        final Object[][] data = new Object[][] {
            { "2012-05-08 19:00:00", 
                "UTC", "Europe/London", "2012-05-08T18:00:00" },
            { "2012-05-08 17:00:00", 
                "Europe/London", "UTC", "2012-05-08T18:00:00" },
            { "2012-05-08 20:00:00", 
                "UTC", "CET", "2012-05-08T18:00:00" },
            { "2012-05-08 19:00:00", 
                "America/Tijuana", "CET", "2012-05-08T10:00:00" },
            { "2012-11-08 21:00:00", 
                "Europe/London", "Asia/Dubai", "2012-11-08T17:00:00" },
            { "2012-11-19 2:00:00", 
                "Europe/London", "Asia/Tokyo", "2012-11-18T17:00:00" } };
        return Arrays.asList(data);
    }

    @Test
    public void test() {
        assertEquals(expectedDatetime, 
            convertTimeZones(fromTimezone, toTimezone, inputDatetime));
    }
}