How do I sort a list by different parameters at different timed

I think your enum approach is basically sound, but the switch statements really need a more object oriented approach. Consider:

enum PersonComparator implements Comparator<Person> {
    ID_SORT {
        public int compare(Person o1, Person o2) {
            return Integer.valueOf(o1.getId()).compareTo(o2.getId());
        }},
    NAME_SORT {
        public int compare(Person o1, Person o2) {
            return o1.getFullName().compareTo(o2.getFullName());
        }};

    public static Comparator<Person> decending(final Comparator<Person> other) {
        return new Comparator<Person>() {
            public int compare(Person o1, Person o2) {
                return -1 * other.compare(o1, o2);
            }
        };
    }

    public static Comparator<Person> getComparator(final PersonComparator... multipleOptions) {
        return new Comparator<Person>() {
            public int compare(Person o1, Person o2) {
                for (PersonComparator option : multipleOptions) {
                    int result = option.compare(o1, o2);
                    if (result != 0) {
                        return result;
                    }
                }
                return 0;
            }
        };
    }
}

An example of usage (with a static import).

public static void main(String[] args) {
    List<Person> list = null;
    Collections.sort(list, decending(getComparator(NAME_SORT, ID_SORT)));
}

You can create comparators for each of properties you might want to sort and then try "comparator chaining" :-) like this:

public class ChainedComparator<T> implements Comparator<T> {
    private List<Comparator<T>> simpleComparators; 
    public ChainedComparator(Comparator<T>... simpleComparators) {
        this.simpleComparators = Arrays.asList(simpleComparators);
    }
    public int compare(T o1, T o2) {
        for (Comparator<T> comparator : simpleComparators) {
            int result = comparator.compare(o1, o2);
            if (result != 0) {
                return result;
            }
        }
        return 0;
    }
}

One way is to create a Comparator that takes as arguments a list of properties to sort by, as this example shows.

public class Person {
    private int id;
    private String name, address;

    public static Comparator<Person> getComparator(SortParameter... sortParameters) {
        return new PersonComparator(sortParameters);
    }

    public enum SortParameter {
        ID_ASCENDING, ID_DESCENDING, NAME_ASCENDING,
        NAME_DESCENDING, ADDRESS_ASCENDING, ADDRESS_DESCENDING
    }

    private static class PersonComparator implements Comparator<Person> {
        private SortParameter[] parameters;

        private PersonComparator(SortParameter[] parameters) {
            this.parameters = parameters;
        }

        public int compare(Person o1, Person o2) {
            int comparison;
            for (SortParameter parameter : parameters) {
                switch (parameter) {
                    case ID_ASCENDING:
                        comparison = o1.id - o2.id;
                        if (comparison != 0) return comparison;
                        break;
                    case ID_DESCENDING:
                        comparison = o2.id - o1.id;
                        if (comparison != 0) return comparison;
                        break;
                    case NAME_ASCENDING:
                        comparison = o1.name.compareTo(o2.name);
                        if (comparison != 0) return comparison;
                        break;
                    case NAME_DESCENDING:
                        comparison = o2.name.compareTo(o1.name);
                        if (comparison != 0) return comparison;
                        break;
                    case ADDRESS_ASCENDING:
                        comparison = o1.address.compareTo(o2.address);
                        if (comparison != 0) return comparison;
                        break;
                    case ADDRESS_DESCENDING:
                        comparison = o2.address.compareTo(o1.address);
                        if (comparison != 0) return comparison;
                        break;
                }
            }
            return 0;
        }
    }
}

It can then be used in code for instance like this:

cp = Person.getComparator(Person.SortParameter.ADDRESS_ASCENDING,
                          Person.SortParameter.NAME_DESCENDING);
Collections.sort(personList, cp);

One approach would be to compose Comparators. This could be a library method (I'm sure it exists somewhere out there).

public static <T> Comparator<T> compose(
    final Comparator<? super T> primary,
    final Comparator<? super T> secondary
) {
    return new Comparator<T>() {
        public int compare(T a, T b) {
            int result = primary.compare(a, b);
            return result==0 ? secondary.compare(a, b) : result;
        }
        [...]
    };
}

Use:

Collections.sort(people, compose(nameComparator, addressComparator));

Alternatively, note that Collections.sort is a stable sort. If performance isn't absolutely crucial, you sort be the secondary order before the primary.

Collections.sort(people, addressComparator);
Collections.sort(people, nameComparator);