How to store more than one string in a Map?

You're in object denial. You should use an object that holds the number, name, address, phone (maybe you could call it ContactInformation) and put that into the map.

No. a Map has only one key. If you want your value to contain more information, wrap the strings in a new class:

public class PersonalInfo {
   private final String name;
   private final String address;
   private final String phone;

   // constructor and getters
}

map.put(number, new PersonalInfo(name, address, phone));

The 'correct' solution is to use an object that holds the values in named fields, but in the spirit of answering the question asked, a simple (if unclean) solution would be to use:

Map<String,List<String>> yourMap = new HashMap<String,List<String>>();

List<String> info = new ArrayList<String>();
info.add(number);
info.add(name);
info.add(address);
info.add(phone);

yourMap.put(key, info);

Note google-collections has a series of classes that implement this structure right out of the box called ListMultimap and it's implementation ArrayListMultimap